How to assign printscreen button to flameshot

After complete removal, you installed with

sudo apt install flameshot

?
And it won't launch?

exactly, I run the terminal install without any errors. flameshot is visible under "Graphics" and when I click nothing happens

In terminal, what does

flameshot configure

show?
How about

flameshot gui

Additionally:
This post says

SOLVED: I resolved this by resetting my locales (since my system wasn't able to locate LC_ALL) and desktop launch option. Go to: System Settings > Regional Settings > Reset all and then set desktop launcher to Exec=flameshot gui in /usr/share/applications/flameshot.desktop .

Might be worth trying, too.

flameshot config works well

flameshot gui - the screen begins to dance and changes resolution etc.

the steps out of that article I did not understand and I think I have to stop here for now. I will look into that again, hopefully with more success.

What I also noticed: installing via software as flatpack brings up another (newer?) version with different setup menu

I am at a loss. I would suggest contacting the Flameshot Developer on this one...

Flatpak can be seen as using the Rolling Release. So it is likely a latest release.
You might try installing the Flatpak version and see if it behaves properly.