In response to your update, the individual setting with the program is a sort of “override” to the defaults.
If you go into:
Steam menu at top > settings > compatibility
You should see options for:
enable steam play for supported titles
enable steam play for all other titles
run other titles with [proton 8.0-5]
To the best of my knowledge, any title which is pre-checked by Steam (and has a green tick or whatever) is covered by the first option - this will automatically install and run using the version of Proton it was first confirmed to run with. If it ran fine with Proton 3.0-0 or whatever when it was first tested, it possibly still uses that version. Some certainly get rechecked with newer versions. It’s worth noting this is confirmed to work on Steam Deck (with its AMD graphics) - sometimes the default checked version will not work so well when you play on the desktop.
The second option allows you to set a default Proton version for all other titles - if you’ve not adjusted this, it’s possibly set on an older version.
You can override this on a game by game basis (as you have been doing already) - for example, on some games, steering wheel controllers work on 6.3-8, but not the newer version 7/8 etc. So my default is everything runs on the newest Proton, except I override some driving games to run on an older version.
[Edit]The point of this being, Cyberpunk, as a confirmed working game, will have defaulted to the version which works with the Steam Deck, without you doing anything (Leaving the “run with steam play” unticked) - that version may not be best suited to a desktop/laptop running Nvidia graphics. Changing the version manually overrides the default version… and I hope it’s all working well for you :) [End edit]
There’s a brilliant and in depth guide on the gamingonlinux website, which is definitely worth a read if you’ve got time: Gamingonlinux Steamplay guide