Linux compatibility is fine. You can pretty easily install gog games by logging into your gof account on lutris. It’ll let you see your whole library and install directly from it, and any games that work in proton will work just fine using proton via lutris. You can also just add your gog game as a non-steam game and run it there.
They just won’t function properly. There are permissions problems and while some games might work, you will run into games that simply won’t launch, or that have regular crashes, among other issues. I recommend installing the games you want to play on Linux there, and the ones you can’t on windows.
Just putting the ISO directly into the ventoy folder on the USB should just work, it’s odd that you had to mount it and drag the files. If you’re trying to use games installed on one drive between windows and Linux, I do not recommend attempting that. Windows can’t natively read Linux drive formats like ext4, and if you try to play games on an NTFS drive on Linux you WILL run into problems. Your cloud saves should just work normally though.
I’ve had a lot of success using Ventoy for my USB drive writing needs. Every steam game has it’s own folder for it’s virtual windows directory. You want to look in /home/your_name/.steam/steamapps/compatdata The folders are all strings of numbers, each being the ID of the respective steam game. You can find the ID for any steam game just by going in it’s store page and looking at the URL. You don’t usually need to mess with this though, just browse the game files in your /steam/common folder.
You can select to run them in proton, rather than just normal wine, in lutris. I’ve been doing it to run games from gog for years with few issues, namely games that are old and have the same problems working on windows as well. So… Yes they will?