Interesting, @Atjowt. I would make the wall edges a little thicker than visual so in riding the edge the whole screen doesn't just turn white.

You might also use a dithering pattern instead of color changes based upon distance of solid objects.

Included in the Pico-8 Demos is a 3D cart that you could find of interest, "cast.p8"

Additional to this, here are 2-pages of Pico-8 carts written by others dealing with raycasting 3D rooms.

https://www.lexaloffle.com/bbs/?sub=0&tag=raycasting#sub=0&search=raycast