TYPO3 Core

For me this works. I tested in v9 and v10 master.
Can you provide a specific setup where this happens to you?

ext_tables.php:
$GLOBALS['TYPO3_CONF_VARS']['SC_OPTIONS']['typo3/backend.php']['constructPostProcess'][] = \[Vendor]\[Ext]\Hooks\BackendStyles::class.'->addCss';

typo3conf/ext/[Ext]/Classes/Hooks/BackendStyles.php:
[...]
$pageRenderer = GeneralUtility::makeInstance(\TYPO3\CMS\Core\Page\PageRenderer::class);
$cssPath = ExtensionManagementUtility::extPath('[Ext]').'Resources/Public/Css/Backend/';
$pageRenderer->addCssFile($cssPath.'bv.css');
[...]

Output:
1.
/typo3/index.php?route=%2Fmain[...] (the main BE page):
[...]
<link rel="stylesheet" type="text/css" href="/typo3conf/ext/[Ext]/Resources/Public/Css/Backend/bv.css" media="all">
[...]

2.
/typo3/index.php?route=%2Fweb%2Flist%2F[...] (the list_frame/typo3-contentIframe inside the main BE page):
No bv.css!

Hard coded solution:
/typo3/sysext/backend/Classes/Template/ModuleTemplate.php:
protected function loadStylesheets() {
[...]
$cssPath = ExtensionManagementUtility::extPath('[Ext]').'Resources/Public/Css/Backend/';
$pageRenderer->addCssFile($cssPath.'bv.css');
[...]
}

Output:
1.
/typo3/index.php?route=%2Fmain[...] (the main BE page):
No bv.css!

2.
/typo3/index.php?route=%2Fweb%2Flist%2F[...] (the list_frame/typo3-contentIframe inside the main BE page):
[...]
<link rel="stylesheet" type="text/css" href="/typo3conf/ext/[Ext]/Resources/Public/Css/Backend/bv.css" media="all">
[...]

Hello,

thank you for your code example!
The hook you used is only executed in the main function of the BackendController. Once The PageRenderer renders the final html he resets all added Css.
After that the current submodule starts the rendering again without your css.
This means you need to register your css globally.
Typo3 Backend uses this global array to register its backend.css:

$GLOBALS['TBE_STYLES']['skins'][] = [
    'stylesheetDirectories' => [
       'EXT:your_ext/Resources/Public/Css/Backend/'
    ]
];

Putting this in your ext_tables.php should do the trick!

Yes, this would do the trick, but not for different user groups, as I think. In my first statement I wrote:

The assignment via $GLOBALS['TBE_STYLES']['skins'] injects the file in both, the main page and the iframe. But with that one cannot assign different files
dynamically depending e.g. on a user group.

Or is that possible via an alternative way?

This does the trick:

$GLOBALS['TYPO3_CONF_VARS']['SC_OPTIONS']['t3lib/class.t3lib_pagerenderer.php']['render-preProcess'][] = \VENDOR\NAME\Hooks\BackendStyles::class . '->addCss';

Your BackendStyles Class:

<?php

namespace VENDOR\NAME\Hooks;

use TYPO3\CMS\Core\Utility\GeneralUtility;

class BackendStyles
{
    public function addCss($params, $ref)
    {
        // The global BE_USERS array is available here and you can add your additional conditions.
        if (TYPO3_MODE == 'BE') {
            $ref->addCssFile(GeneralUtility::getFileAbsFileName('EXT:your_ext/Resources/Public/Css/Backend/bv.css'));
        }
    }
}

I hope this helps!

Yes, it works, great!
Thank you very much!