Shift+Tab is pretty common to press during gameplay, as to look up ingame statistics while running! ;-)
So i would like to change that, i don't fear .ini or other file edits, i just have no idea where to search for - any help would be apprechiated :-)

If only it were that easy. I suggest looking for the reverse: a way to reassign keyboard shortcuts in the game. As far as I know, there's no way to remap GOG Galaxy's keyboard shortcuts, though I certainly wouldn't mind being proven wrong. The configuration file is %LocalAppData%\GOG.com\Galaxy\Configuration\config.json and as you can see, there's nothing in there about keyboard shortcuts. I expect if they weren't hard-coded, there would be a way to change them in the UI.

The thorn in my side is the F12 key. It's typically used as a screenshot key by both games and GOG Galaxy, and it can't be changed in either. When this happens, I not only end up with double screenshots, but botched double screenshots, since the notification that a screenshot has been taken becomes part of the screenshot.
A suggested workaround for this that's floating around is to change the permissions for the screenshots folder, so that files can't be written there. This is something I wont do, but directions are in the comments below if you're interested.

You can click the cog wheel icon in the top left to submit feedback, and you can vote for these community wishes:
Take in-game screenshots with rebindable key
Rebindable Hotkeys (Screenshot, Overlay and whatever may comes...)
Rebindable Overlay and Screenshot Keys

Well, "overlay.js" in "...\Program Files\GOG Galaxy\web" looks promissing, but is a single line script and horrible to read - maybe someone else with more knowledge about java could make some clues out of it - but i rather opt to just deactivate that "feature" (that doesn't even has a browser, so i need to Alt-Tab anyway! xP) entirely, until GoG makes something useful out of it!

But thank's for the Clues, always gl:hf! :-)

i guess only option is to just delete the file so there no key binding huh ?

I looked up this question about over lay people been complaining about it sense 2016

I think people need to stop posting on forms and start request it as a feature to there support.

https://support.gog.com/hc/en-us/requests/new?product=gog&form=technical&_gl=1*1utaoi0*_gcl_au*MTk0MzA4NzAzMS4xNjk4NzEyODg5

I sent request in my self I think only way this will get fixed is if more people send them tickets about it

steam and UBI and even EA have abilty to rebind overlay keys no reason GOG cant.

in all my game store client software I always bind it to Alt + enter