I know this is a subject that is mentioned often, but the articles I find are very old. Can I play The Witcher 3 on Linux, and if so will my save game that I have on GOG transfer using the cloud

For non-native Linux games on GOG (like the Witcher 3), you are left to go look for 3rd party 'tools' to get the game running on Linux. There's quite a number of ways to do that, many from GOG users alone, around here, which is awesome.

But it all basically means WINE in one way or another, possibly multiple times. I strongly recommend looking up those readymade scripts/workarounds/wrappers to install Witcher 3.

I'll tell you about my recent experience a little bit though - I was unaware of some of the present GOG user tools, too, in the beginning.

So, unfortunately, GOG Galaxy does not have a Linux version, but you can WINE Galaxy itself.

For example, from my personal experience, I used Lutris (if you don't know, it provides readymade installation scripts for WINE, and applies fixes and workarounds to get games/clients running) to run GOG Galaxy. Then I just installed Witcher 3 through there, and played it enough to make sure it's working well.

Before I tried Galaxy, I tried a different way. I manually downloaded the offline installers and used WINE to run the installer for Witcher 3. And then manually patched the game, again with WINE. Then used WINE to run the game. This also worked, though it took much longer to install, and seems more of a hassle.

TLDR - I don't recommend doing the thing manually, and not using the available 'tools' present on these forums for example.

That cloud thing is what demands Galaxy, which sometimes does and sometimes does not work in Wine. You can always just copy over the save(s) yourself.