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After much testing, I cracked using the GOG build with Proton:

• The msxml3 winetrick is required; protontricks[1] will help you apply this easily. (It is well-compatible with Flatpak.)
• ALTERNATIVELY: If you don't want to use protontricks, you can have it automatically applied by creating a file called "steam_appid.txt" next to each one of the game's main executables; this file should contain nothing but a single number: 34460 for BtS, 3900 for the base game, and 16810 for Colonization.
• If you are not using the steam_appid method, you must set the launch options: 「WINEDLLOVERRIDES="msxml3=n" %command%」 (without brackets).
• If you are using the steam_appid method and your GPU is pre-Vulkan (AMD ~2013; NVidia ~2012), then instead set PROTON_USE_WINED3D=1 launch env.

Stuff you might want to do or know:
• To make it easier to manage which expansion you're playing, I highly recommend installing the game itself to a location somewhere outside the prefix, such as 「Z:\home\YOURNAMEHERE\.local\share\Steam\nonsteam\Sid Meier's Civilization IV」. (Additionally, Steam does NOT appear to delete its own internal compatdata folders when you remove 3rd-party games.)
• If you are OCD about matching the game icon to the window icon, get it from "Civ4[/expansion name]/Assets/res/"
• The game settings are hidden at "steamapps/compatdata/APPID/pfx/drive_c/users/steamuser/My Documents/My Games/"

Confirmed to be cargo-culting:
any d3d winetrick; GOG takes care of this for you with install-time patches. I am not using any on my current, functioning prefix.
• deleting or renaming the game-bundled copies of msxml3.dll: does nothing that I could identify.
• "msxml3r" override: even if (big if) this originated as anything other than a typo, it does nothing that I could identify.

Links since I'm not allowed to post them on an account this new:
[1] github (dot) com/Matoking/protontricks
[2] google (dot) com/search?q=%22put+the+file+steam_appid.txt+containing+the+correct+appID+in+your+game+folder%22
Post edited June 07, 2022 by squeegily