I am happy to report that it runs perfectly on Proton (tested on 6.21-GE-2). Just add it as a non-steam game to your library (the exe you want is BBPSX-Win64-Shipping.exe), select the compatibility option, and you're good to go :) It is entirely possible that it runs perfect without the GloriousEggroll proton build, feel free to report back with which one you used.
Of course it would be fantastic to have it native on linux, but this is a great workaround for now