Hello chikorina, hello Thunderbolt-GER,
first I tried to clean the game data by using the tool but after pressing the 'clean' button nothing happend. Nothing was cleaned, all save games and settings were preserved, no error message or anything else.
Next, I uninstalled and reinstalled the entire game, but even after reinstalling, the game didn't start.
Finally I was start steam and the game under a different Windows user account and ... it runs.
The name of the Windows user were the game do not start is 'Öffentlich'.
The name of the user were the game runs is 'Privat'.
Since the username is also included in the path, I assume that the game has recently had a problem with letters like 'ä' 'ö' 'ü' and maybe others.
But I'm not absolutely sure because I just tried it with one another Windows user, however this helped me.
@Thunderbolt-GER maybe this will help your teammate too?
@chikorina Thank you again for your help and support so far.