do you want to remember this browser ?

No, it's the one I use for pron... Wait, shit...

I'll clear cookies in 5 minutes so I don't care.

Sounds a bit like Telltale Games: Site will remember that.

Then you come back just a few minutes later and nope, it didn't. After that you log in on the game PC and next day it doesn't remeber that browser either.

Steam seems to really like being annoying like that and require an email token just every time you use it from the game PC. It's literally like they optimized the system for maximum annoyance. Or maybe they just can't imagine people having a seperate PC for gaming (despite them literally selling exactly that as their Steam Deck).