TYPO3 Core

will look into it. At least install acceptance tests are green with postgres 13 / 10.4branch - will do real check later.

One question - composer or legacy installation ?

Sorry to say, I can not confirm this or reproduce this. For Issue #96940 I have done a dozen of installations
with Postgres (manually, not core tests). With v10, v11 and main (v12) and with Postgres 10 and 13. Installation
always executed without any issues through the process entering all the values.

Maybe you can retry this on a clean install ?? Otherwise I do not have a clue how this may come to that issue for
you. No chance to reproduce it yet.

So this is what I did on fresh Debian 11 minimal:

apt install postgresql-13 nginx php7.4 php7.4-fpm php7.4-cli php7.4-common php7.4-curl php7.4-gd php7.4-imap php7.4-intl php7.4-json php7.4-mbstring php7.4-pgsql php7.4-opcache php7.4-readline php7.4-soap php7.4-xml php7.4-zip imagemagick

Edit /etc/php/7.4/fpm/php.ini:

memory_limit = 512M
max_execution_time = 600
max_input_vars = 1500
post_max_size = 10M
upload_max_filesize = 10M

Edit /etc/php/7.5/fpm/pool.d/www.conf:

upload_max_filesize = 10M

Create /etc/nginx/sites-enabled/t3test.conf with the following content:

server {
    listen                  443 ssl http2;
    listen                  [::]:443 ssl http2;
    server_name             t3test.precisma.com;
    set                     $base /var/www/;
    root                    $base/t3test.precisma.com;

    # SSL
    ssl_certificate /etc/ssl/certs/ssl-cert-snakeoil.pem;
    ssl_certificate_key /etc/ssl/private/ssl-cert-snakeoil.key;

    # security
    include                 security.conf;

    # index.php
    index                   index.php;

    # index.php fallback
    location / {
        try_files $uri $uri/ /index.php?$query_string;
    }

    # additional config
    include general.conf;

    # Compressing resource files will save bandwidth and so improve loading speed especially for users
    # with slower internet connections. TYPO3 can compress the .js and .css files for you.
    # *) Set $GLOBALS['TYPO3_CONF_VARS']['BE']['compressionLevel'] = 9 for the Backend
    # *) Set $GLOBALS['TYPO3_CONF_VARS']['FE']['compressionLevel'] = 9 together with the TypoScript properties
    #    config.compressJs and config.compressCss for GZIP compression of Frontend JS and CSS files.
    location ~ \.js\.gzip$ {
        add_header Content-Encoding gzip;
        gzip off;
        types { text/javascript gzip; }
    }
    location ~ \.css\.gzip$ {
        add_header Content-Encoding gzip;
        gzip off;
        types { text/css gzip; }
    }

    # TYPO3 - Rule for versioned static files, configured through:
    # - $GLOBALS['TYPO3_CONF_VARS']['BE']['versionNumberInFilename']
    # - $GLOBALS['TYPO3_CONF_VARS']['FE']['versionNumberInFilename']
    if (!-e $request_filename) {
        rewrite ^/(.+)\.(\d+)\.(php|js|css|png|jpg|gif|gzip)$ /$1.$3 last;
    }

    # TYPO3 - Block access to composer files
    location ~* composer\.(?:json|lock) {
        deny all;
    }

    # TYPO3 - Block access to flexform files
    location ~* flexform[^.]*\.xml {
        deny all;
    }

    # TYPO3 - Block access to language files
    location ~* locallang[^.]*\.(?:xml|xlf)$ {
        deny all;
    }

    # TYPO3 - Block access to static typoscript files
    location ~* ext_conf_template\.txt|ext_typoscript_constants\.txt|ext_typoscript_setup\.txt {
        deny all;
    }

    # TYPO3 - Block access to miscellaneous protected files
    location ~* /.*\.(?:bak|co?nf|cfg|ya?ml|ts|typoscript|tsconfig|dist|fla|in[ci]|log|sh|sql|sqlite)$ {
        deny all;
    }

    # TYPO3 - Block access to recycler and temporary directories
    location ~ _(?:recycler|temp)_/ {
        deny all;
    }

    # TYPO3 - Block access to configuration files stored in fileadmin
    location ~ fileadmin/(?:templates)/.*\.(?:txt|ts|typoscript)$ {
        deny all;
    }

    # TYPO3 - Block access to libraries, source and temporary compiled data
    location ~ ^(?:vendor|typo3_src|typo3temp/var) {
        deny all;
    }

    # TYPO3 - Block access to protected extension directories
    location ~ (?:typo3conf/ext|typo3/sysext|typo3/ext)/[^/]+/(?:Configuration|Resources/Private|Tests?|Documentation|docs?)/ {
        deny all;
    }

    location = /typo3 {
        rewrite ^ /typo3/;
    }

    location /typo3/ {
        absolute_redirect off;
        try_files $uri /typo3/index.php$is_args$args;
    }

    # handle .php
    location ~ [^/]\.php(/|$) {
        fastcgi_split_path_info ^(.+?\.php)(/.*)$;
        if (!-f $document_root$fastcgi_script_name) {
            return 404;
        }

        # this is the PHP-FPM upstream - see also: https://www.nginx.com/resources/wiki/start/topics/examples/phpfcgi/#connecting-nginx-to-php-fpm
    fastcgi_read_timeout 500;
        fastcgi_pass         unix:/var/run/php/php7.4-fpm.sock;
        include      php_fastcgi.conf;
    }
}

# HTTP redirect
server {
    listen      80;
    listen      [::]:80;
    server_name t3test.precisma.com;
    include     letsencrypt.conf;

    location / {
        return 301 https://t3test.precisma.com$request_uri;
    }
}

Full nginx config attached.

Then I restart all services:
systemctl restart php7.4-fpm.service nginx.service postgresql.service

Adding postgres user and database:

root@t3test:~# sudo -u postgres psql
could not change directory to "/root": Keine Berechtigung
psql (13.5 (Debian 13.5-0+deb11u1))
Type "help" for help.

postgres=# CREATE USER t3test WITH PASSWORD 't3testpassword';
CREATE ROLE
postgres=# CREATE DATABASE t3test WITH OWNER t3test;
CREATE DATABASE
postgres=# GRANT ALL ON DATABASE t3test TO t3test;
GRANT
postgres=# \q

Create the Documentroot and where the TYPO3 source goes:

root@t3test:/var/www# mkdir -p /var/www/t3test.precisma.com
root@t3test:/var/www# mkdir -p /var/www/typo3

Download and extract TYPO3:

root@t3test:/var/www/typo3# wget --content-disposition https://get.typo3.org/10.4.25
root@t3test:/var/www/typo3# tar xzf typo3_src-10.4.25.tar.gz

Create symlinks from Documentroot to TYPO3 Source:

root@t3test:/var/www/t3test.precisma.com# chown www-data:www-data /var/www/t3test.precisma.com/
root@t3test:/var/www/t3test.precisma.com# ln -s ../typo3/typo3_src-10.4.25/ typo3_src
root@t3test:/var/www/t3test.precisma.com# ln -s typo3_src/index.php 
root@t3test:/var/www/t3test.precisma.com# ln -s typo3_src/typo3/
root@t3test:/var/www/t3test.precisma.com# ls -la
insgesamt 8
drwxr-xr-x 2 www-data www-data 4096 22. Feb 10:58 .
drwxr-xr-x 6 root     root     4096 22. Feb 10:54 ..
lrwxrwxrwx 1 root     root       19 22. Feb 10:57 index.php -> typo3_src/index.php
lrwxrwxrwx 1 root     root       16 22. Feb 10:58 typo3 -> typo3_src/typo3/
lrwxrwxrwx 1 root     root       26 22. Feb 10:57 typo3_src -> ../typo3/typo3_src-10.4.25/

Then open Firefox and Start the installation.

Then root@t3test:/var/www/t3test.precisma.com# touch FIRST_INSTALL

Step 1 works fine:

Step 2 not working:

This is what the Documentroot looks then:

root@t3test:/var/www/t3test.precisma.com# ls -la
insgesamt 20
drwxr-xr-x 5 www-data www-data 4096 22. Feb 11:03 .
drwxr-xr-x 6 root     root     4096 22. Feb 10:54 ..
drwxrwsr-x 4 www-data www-data 4096 22. Feb 11:03 fileadmin
-rw-r--r-- 1 root     root        0 22. Feb 11:03 FIRST_INSTALL
lrwxrwxrwx 1 root     root       19 22. Feb 10:57 index.php -> typo3_src/index.php
lrwxrwxrwx 1 root     root       16 22. Feb 10:58 typo3 -> typo3_src/typo3/
drwxrwsr-x 5 www-data www-data 4096 22. Feb 11:03 typo3conf
lrwxrwxrwx 1 root     root       26 22. Feb 11:01 typo3_src -> ../typo3/typo3_src-10.4.25
drwxrwsr-x 4 www-data www-data 4096 22. Feb 11:03 typo3temp

and

root@t3test:/var/www/t3test.precisma.com/typo3conf# ls -la
insgesamt 28
drwxrwsr-x 5 www-data www-data 4096 22. Feb 11:03 .
drwxr-xr-x 5 www-data www-data 4096 22. Feb 11:03 ..
drwxrwsr-x 2 www-data www-data 4096 22. Feb 11:03 ext
drwxrwsr-x 2 www-data www-data 4096 22. Feb 11:03 l10n
-rw-rw-r-- 1 www-data www-data 1239 22. Feb 11:03 LocalConfiguration.php
-rw-rw-r-- 1 www-data www-data 3010 22. Feb 11:03 PackageStates.php
drwxrwsr-x 2 www-data www-data 4096 22. Feb 11:03 sites

I attached the complete Documentroot as tgz.

The nginx logs:

root@t3test:/var/www/logs/nginx# cat access.log 
192.168.1.175 - - [22/Feb/2022:10:59:32 +0100] "GET / HTTP/1.1" 301 162 "-" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:10:59:36 +0100] "GET / HTTP/2.0" 302 0 "-" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:10:59:36 +0100] "GET /typo3/install.php HTTP/2.0" 200 567 "-" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:10:59:36 +0100] "GET /typo3/install.php?install[action]=mainLayout HTTP/2.0" 200 333 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:10:59:36 +0100] "GET /typo3/install.php?install[action]=checkInstallerAvailable HTTP/2.0" 200 37 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:10:59:36 +0100] "GET /typo3/install.php?install[action]=showInstallerNotAvailable HTTP/2.0" 200 379 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:02:21 +0100] "GET / HTTP/2.0" 302 0 "-" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:02:21 +0100] "GET /typo3/install.php HTTP/2.0" 200 523 "-" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:02:22 +0100] "GET /typo3/install.php?install[action]=mainLayout HTTP/2.0" 200 331 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:02:22 +0100] "GET /typo3/install.php?install[action]=checkInstallerAvailable HTTP/2.0" 200 37 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:02:22 +0100] "GET /typo3/install.php?install[action]=showInstallerNotAvailable HTTP/2.0" 200 379 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:36 +0100] "GET /typo3/install.php HTTP/2.0" 200 523 "-" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:37 +0100] "GET /typo3/install.php?install[action]=mainLayout HTTP/2.0" 200 331 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:37 +0100] "GET /typo3/install.php?install[action]=checkInstallerAvailable HTTP/2.0" 200 36 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:37 +0100] "GET /typo3/install.php?install[action]=checkEnvironmentAndFolders HTTP/2.0" 200 37 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:37 +0100] "GET /typo3/install.php?install[action]=showEnvironmentAndFolders HTTP/2.0" 200 524 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:57 +0100] "GET /typo3/install.php?install[action]=executeEnvironmentAndFolders HTTP/2.0" 200 36 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:57 +0100] "GET /typo3/install.php?install[action]=checkTrustedHostsPattern HTTP/2.0" 200 36 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:57 +0100] "GET /typo3/install.php?install[action]=executeSilentConfigurationUpdate HTTP/2.0" 200 37 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:57 +0100] "GET /typo3/install.php?install[action]=executeSilentConfigurationUpdate HTTP/2.0" 200 36 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 
192.168.1.175 - - [22/Feb/2022:11:03:57 +0100] "GET /typo3/install.php?install[action]=checkDatabaseConnect HTTP/2.0" 500 0 "https://t3test.precisma.com/typo3/install.php" "Mozilla/5.0 (X11; Fedora; Linux x86_64; rv:97.0) Gecko/20100101 Firefox/97.0" 

root@t3test:/var/www/logs/nginx# cat error.log 
2022/02/22 11:03:57 [error] 18799#18799: *4 FastCGI sent in stderr: "PHP message: PHP Fatal error:  Uncaught Error: Call to undefined function mysqli_init() in /var/www/typo3/typo3_src-10.4.25/vendor/doctrine/dbal/lib/Doctrine/DBAL/Driver/Mysqli/MysqliConnection.php:64
Stack trace:
#0 /var/www/typo3/typo3_src-10.4.25/vendor/doctrine/dbal/lib/Doctrine/DBAL/Driver/Mysqli/Driver.php(16): Doctrine\DBAL\Driver\Mysqli\MysqliConnection->__construct()
#1 /var/www/typo3/typo3_src-10.4.25/vendor/doctrine/dbal/lib/Doctrine/DBAL/Connection.php(362): Doctrine\DBAL\Driver\Mysqli\Driver->connect()
#2 /var/www/typo3/typo3_src-10.4.25/typo3/sysext/core/Classes/Database/Connection.php(101): Doctrine\DBAL\Connection->connect()
#3 /var/www/typo3/typo3_src-10.4.25/vendor/doctrine/dbal/lib/Doctrine/DBAL/Connection.php(428): TYPO3\CMS\Core\Database\Connection->connect()
#4 /var/www/typo3/typo3_src-10.4.25/vendor/doctrine/dbal/lib/Doctrine/DBAL/Connection.php(388): Doctrine\DBAL\Connection->getDatabasePlatformVersion()
#5 /var/www/typo3/typo3_src-10.4.25/vendor/doctrine/dbal/lib/Doctrine/" while reading response header from upstream, client: 192.168.1.175, server: t3test.precisma.com, request: "GET /typo3/install.php?install[action]=checkDatabaseConnect HTTP/2.0", upstream: "fastcgi://unix:/var/run/php/php7.4-fpm.sock:", host: "t3test.precisma.com", referrer: "https://t3test.precisma.com/typo3/install.php" 

And the Firefox Console:

I hope this is reproduceable eith this information.

I just added the php7.4-mysql package and then step 2 looks ok.

With TYPO3 11 there is no problem without the php-mysql installed.

I tried with v11 and there is no problem.
In Step 2 it also selects Postgresql as default.

If php-mysql is installed it defaults to a mysql-connection in step 2

I have retest all and also tested the mentioned patch (which mitigates this issue).

So, to sum this up what happens here:

If no mysql mysqli php is not installed, installation will fail through a error in the database ready/complete check.
Thus writing invalid part configuration and failing hard, not providing the correpsonding driver selection.

Anyway, the already meantioned patch https://review.typo3.org/c/Packages/TYPO3.CMS/+/71514 from issue #95545 changes
exactly that check. I have retested this with v10 WITHOUT installed mysql(i) php extensin and could complete the full
installation process with postgres as expected.

The patch original was marked for backport, which has not been done (yet). Will ping someone from the core team on that
if we can backport that patch to v10. Still, v10 is in priority bugfix with no scheduled releases anymore, so even if it
got backported is open when a new release will be done. Currently the patch applies without hassle on v10 and works. So
at least creating a composer patch would work for composer based installations.

Hey. After a couple of month without further feedback I assume this is resolved. I hope it's ok to close here.