I don’t think that’s distro related. I’ve played GW2 on Mint with an Nvidia card and it worked just like on Windows. I installed the Steam version though and linked my account.

What Proton version are you using in Steam to play it, did you try some different ones? Without knowing what your issue really is, there are some tinker steps mentioned on ProtonDB, maybe have a look. It’s really hard to recommend anything without more info.