

Works perfectly out of the box
Turned out that problems I had earlier were completely on my side (couldn't start any steam game). After fixing my problem, this game started and played like charm without needing any tinkering.
Game doesn't start with proton 8.0-3, proton 7.0-6 or 6.3-8
Had to launch in desktop mode for first launch to install UE4 prerequisites.
If installing through SteamOS, you will need to set the compatibility options and verify local files after clicking "Install" before the download will begin.

Works out of the box now
Proton 6.3-6 includes a fix for the Unreal installer that avoids any need for tinkering, making the game fully functional out of the box.

Freezes on fast mode. Solved by turning off motion blur in accessibility settings.
When pressing "F" for fast mode, game froze and I had to reboot it. This was able to be solved by turning off motion blur in accessibility settings. (Thx for NickBell for the help regarding the issue)

Game requires VC Runtime 2019, but the included UE4 redist installer and winetricks both fail to install it correctly. You can replace the UE4 redist installer with a functioning one following these steps (albeit replacing the game's directory name with Temple Of Snek): https://github.com/ValveSoftware/Proton/issues/4138#issuecomment-850575335
In addition, the game ships an empty Linux depot. You'll have to manually select a Proton version via the standard properties dialog for the game to download correctly.

Tries to install Visual C++ Runtime via UE4 and fails with "Invalid ACL"
Attempted Proton 5.13-6 as well as 6.3-5 and 5.21-GE-1
Per Google, attempted protontricks vcrun2015
but that was unavailable in my winetricks; someone else may have more luck. Someone better at Tinkering / with more time to devote may have more success.