What distro are you using for Linux? Civ 6 is literally the only reason I keep my Windows partition and I can't get civ 6 to work with Proton.
I just checked and it turns out it's running natively not via proton.
Not sure if any of this will be news to you, but for generally debugging:
If you run `steam` from a command line, and then launch civ 6 (or any game) from steam, it will print any errors to the terminal. Chances are it's some sort of missing dependency.
I was told by someone else that I might need to set launch options to `LD_PRELOAD=/usr/lib/libfreetype.so.6 %command%`, for whatever reason I didn't need to, but you might try that.
The two most important factors for a game to run well are 1) the version of Wine/Proton you're using and 2) the version of your GPU driver you're using.
Rolling release distros like Arch are great for gaming, since you always have the last version of Wine and of your GPU driver. It's a real pain in comparison on fixed release distros like Ubuntu, especially if like me you stick with LTS releases.
By using Proton within Steam Play you at least don't have to worry much about the version of Proton; just make sure you've not forced an old release and Steam will chose the right one for you. Same when using Wine within Lutris. Your only remaining duty is to make sure you're running up-to-date GPU drivers.
Civ 4 runs on wine, but the Beyond the Sword expo needs workarounds to work (some few winetricks commands). Does not run out of the box.
Civ 4 Colonization works out of the box but occassionally it will hang.
I have not tried Civ 3 or previous civs.
FreeCiv/FreeCol can be fun too if you don't mind the graphics. Especially the online play. The diplomacy is different.