Here's my setup:
I have Kubuntu 22.04 and Witcher 3 on GOG. I couldn't get Witcher 3 to work on GOG in Kubuntu with WINE - there were major video issues (like watching a slideshow).

I could get GOG to work by adding the GOG installer as a non-Steam game and installing it. Then I added the GOG executable to Steam as a non-Steam game using Proton Experimental. I could then launch GOG and install Witcher 3.

However, when I tried to launch Witcher 3 through GOG (running through Proton Experimental) I have no mouse. There is not even a mouse pointer. However, the keyboard appears to work.

If I add the Witcher 3 executable to Steam and launch it with Proton Experimental everything works perfectly. However, I don't get any of the achievements or other GOG goodies.

Why would the mouse not be recognized or available if I try to run Witcher 3 through GOG and Proton Experimental? Is there a way to get it to work?

I'm assuming you mean the proton linux build and not something referencing proton vpn (or another of that seperate entities services)?
Context is important.

Yeah. Galaxy through Wine.

Just don't.

Good call, I meant Proton Experimental Compatibility through Steam.

I wonder if the client is somehow stealing the mouse focus away from the game. I wish I knew so I could help. I wish GOG had Linux support so their "DRM Free" loving customers weren't pushed under Microsoft's "Anti-DRM Free" ecosystem.

Strange

Well, im not of much more use here (have only used that proton once or twice to no good effect some time ago), but at least its def clear for anybody that can help. Hope you find a fix! :)

About a year ago I decided to switch to Ubuntu/Kubuntu as my main desktop for gaming and it's worked out far better than I expected. I found that with Steam and Proton I can get not only almost every Windows game to work perfectly, but other Windows programs as well. I find that they work even better than using WINE in pretty much every case by adding them to Steam as a non-Steam game.

The Witcher 3 issues I mentioned in this thread are a rare exception. It likely has to do with going through the GOG client. But like I mentioned, if I open the Witcher 3 executable directly in Steam there are no issues at all.

I have a few wild guesses:
Are you in an X/Wayland session?
Are you trying to launch it without a virtual desktop? Some games would prefer the virtual desktop.

I get no such issue with The Witcher 3, but I use neither GOG Galaxy, Steam nor Proton.

Instead I installed the game using ./play.it, that relies on the distro-provided build of WINE (8.0 on my Debian Sid) + DXVK installed through winetricks.

I commend you for your efforts :) I think it's great, but OP did want achievements.

As far as I know, that's currently only possible through Galaxy. Though apparently it's coming to Heroic and Lutris.

Getting Galaxy to run via Wine is a pain though (to OP and anyone else interested) last I checked. I tried it with Wine 7.x, I guess last year, it was wonky and janky and commonly resulted in some error XX from Galaxy when installing some games (including Witcher). For others it did manage to run though, like XCOM2.

The approach of using Proton through non-Steam game isn't that useful either. Proton integrates with Steam games and has it's workarounds and Vulkan shader solution built-in in that ecosystem.

Why not just use Heroic/Lutris/Bottles/.play.it scripts/own custom wine-staging prefix? Why rely on the Steam client and complicate things even more, OP? I don't see any benefit, but maybe I'm missing something.

Valve would not bother with any fixes for Galaxy through Proton. At least, I doubt that.