I'm going slightly mad!
Just switched the non working installation from PHP 7.4 to PHP 8.0.14 as a test. Result was an error:
Warning: Undefined array key "icon_max_size"
After switching back to PHP 7.4, I was able to log in again. And ... TADAAAAA ... now it runs correctly.
Ah ... ok ... I think it's the "Forward after login" setting. The portal type must be set to "Standalone" if the redirection after login to the front page should work correctly. Or respectively, with the setting, calling the forum works again.
But still got undefined-sub-action-errors on adding downloads or galleries.