OMG I think I am stupid to some degree or I was just too tired back then from the struggles, I was in the middle of writing you answer with questions etc. but then I read your reply once again about you not knowing why it would behave differently, so I went back to obs to check on it and to my surprise It actually worked. Maybe not directly but thanks for opening my eyes and helping me out!Unfortunately, I am not sure I exactly understand what the problem is.
What exactly is "app" referring to here?
The "Honkai Star Rail game" or something else?
To be honest I am not sure why what you have set up would behave differently depending on if an application is fullscreen or not.
Does "Honkai Star Rail game" maybe change its window title when it switches to fullscreen mode?