Ashes 2063 - An extremely polished post apocalyptic Doom conversion complete with drivable motorcycle, trading towns, a John Carpenter-esque soundtrack, and it's free!

The Standalone release is Windows only, but I can confirm it works just fine with Proton in steam after adding it as a non-steam game.

Alternatively, you can download the .Pk3 version, which allows you to run it natively through the Linux version of GZDoom.

Really recommend giving it a try, it's a fantastic little game with a lot of effort put into it. The gunplay feels great, the environments and art are awesome, and the level design is solid.