Okay, this is kind of a stab in the dark, but I'm wondering if anyone might know where to look for my save data.
My OS is Bazzite, I play VotV through Steam using Proton 9.0 compatibility tools.

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Hi fellow penguin enjoyer.
Navigate to /home/<user>/.steam/steam/steamapps/compatdata
Here it's a guessing game as the numbers are pretty much random, but if you don't have that many games it should be easy.
In the right folder navigate to /pfx/drive_c/users/steamuser/AppData/Local
If it's the right folder you should see a VotV folder here.
Inside it in /Saved/SaveGames
Cheers!
I haven't used Steam for games that aren't on Steam, but at least for Steam games, Steam uses a SteamLibrary folder (the one a specific game is installed under). The steamapps folder you mention is indeed the default directory, so probably the place where things go by default, but it might be a different SteamLibrary folder if a different one is set as the default.
The numbers are just the store/app ID (the one you see on store page URLs), so no clue what it does for non-Steam games. I've heard that the longest numbers are for non-Steam stuff, but not sure if that's true.
Edit: Also, handy to mention, a tilde (~) is automatically the home directory, and might be quicker/easier for navigation than using the root path.