IIRC, Steam has a great service called Proton that runs Windows-only games in a type of Linux compatibility mode or something.

Is that any better than running Cyberpunk 2077 through GOG using other means on Linux?

It's not native so it's not as good as the software it was programmed for - in this case.

Recently, there has been some good updates on custom versions of proton such as from Glorious-egg which has increased it's fps from previous versions, but generally it lags behind.

I would recommend to use that if you have at least a mid, mid-high gig. Low end works as well, but don't expect miracles.

Edit#
There is no difference between GOG and Steam versions. You can use the same Proton versions, there won't be any differences.

I don't have CP2077 yet, because there is no official Linux port - to end users.

What I know:
a) Proton is basically a pimped WINE. Yes, Valve does actively care for it. And a lot of games are known to run well there.
b) There should be a Linux port - but yet it seems to be exclusive to Stadia. Stadia is Google's streaming stuff, you stream the game. However, afaik their machinery is 100% Linux running amdgpu drivers and thus AMD hardware. So yes, there is a Linux port, but only Google has it. And you can't since it runs on their servers and you're just reduced to a thin client that sends driving signals and receives an image.

So in theory it should be working, just CDPR didn't release this to the public. You could hope and wait for a later release or try your luck with WINE.

Or just buy on steam. And write GOG/CDPR an email that you either refuse to buy at all or that you were spending 30% "tax" into Valve's purse and not directly to CDPR because of their bad service for Linux users.

Proton is a fork of DXVK. I think Valve contracted the DXVK developers? But I may be wrong on that last statement. DXVK was a fort of Wine, which used Vulkan Renderer instead of OpenGL. It does get updated heavily.

There is a database called ProtonDB that does keep track of Proton compatibility. Here's the entry for Cyberpunk :

https://www.protondb.com/app/1091500

You're saying I can play Cyberpunk in Steam's Proton technology even if I bought my Cyberpunk game from GOG? If so, that would pretty much solve my problem.

It does work. Here's how:

1. Run these commands one line at a time in a terminal (If you use Ubuntu or similar, press Ctrl+Alt+T):
sudo add-apt-repository multiverse
sudo apt update && sudo apt upgrade
sudo apt install steam

2. Open Steam
3. Log in
4. Steam > Settings > Steam Play and turn on "Enable Steam Play"
5. If Proton is all you want to use, do this, but if you want to use different versions, or enable Wine for some games, skip this: Enable for all titles.
6. Close Settings and restart Steam
7. Go to Tools in Library and install the latest Proton

Add Cyberpunk 2077:
8. From the Games menu choose "Add a Non-Steam Game to My Library"
9. Browse to and select Cyberpunk 2077 (You might need to switch the view to All Files to see .exe files.)
10. If you skipped 5, then right-click Cyberpunk 2077 once it's in your library and choose "Properties"
11. Select "Force the use of a specific Steam Play compatibility tool" to use the Proton instead of the system default Wine. Select the desired Proton version from the drop down menu.

Has anyone here run it in Wine?

Yes, people tried to run it (see the Wine's AppDB for Cyberpunk 2077). Unfortunately, most attempts failed (with the rating "garbage"). One person made it work for the game version 1.04. However, it had problems: "huge performance issues and blinking lights".

You're supposed to relaxen when watschen der blinkenlights.

Why would CDPR make a Linux version and then not even offer it for sale to Linux users and only sell it to Google? How annoying! Ah, a Wine user reports website. Nice find.

Steam Proton user reports for Cyberpunk 2077:
https://www.protondb.com/app/1091500

Your Wine user reports for Cyberpunk 2077:
https://appdb.winehq.org/objectManager.php?sClass=application&iId=20106

Based on the user reports, it looks like a Linux user will have a better experience playing the Steam version in Proton. I guess my question is answered..

Slightly frustrating, because I would like to be buying games in GOG Galaxy app, but I also want to go to Linux.