TYPO3 Core

I've just setup a fresh TYPO3 9.2.1 with composer.

On using the "Maintenance" -> "Manage language packs" backend module I try to get the German language packs. But all packs are reported to be not available:

Language packs updated
0 new language packs downloaded, 0 language packs updated, 22 language packs not available

I digged a little in LanguagePackService.php and I suppose it is the call (currently in line 255) of

GeneralUtility::writeFileToTypo3tempDir($absolutePathToZipFile, $languagePackContent)

Doing this - a little patched - on the console by

/var/www/MYPROJECT/vendor/typo3/cms-cli/typo3 -vvv language:update

leads to

/var/www/MYPROJECT/var/transient/" was not within directory PATH_site + "typo3temp/" 

That's of course true. So what is wrong? TYPO3 9.2 or my directory layout?

I installed TYPO3 the following way:

cd /var/www/MYPROJECT/
composer require typo3/minimal typo3/cms-lang typo3/cms-fluid-styled-content (and other)

Finally my document root == PATH_site is

/var/www/MYPROJECT/public/

Am I wrong or TYPO3 9.2.1?