This mod doesn't seem to be working with either the latest version of forge (forge 36.1.4) or the recommended version of forge (forge 36.1.0). I don't get it, what version of forge is the right one?

Closing due to inactivity.

I'm unable to recreate the issue. It works fine for me on both of those versions. Double check that you have the correct version of the mod installed.

With 36.1.4 I also get the error "File BetterMineshafts-Forge-1.16.4-2.0.3.jar is for an older version of Forge and cannot be loaded"

It would help if you included the version of the mod you are using. I've had those problems before; for example somehow Curse wanted me to update a 1.16.4 mod pack to use a 1.16.5 file and wouldn't let me update to the proper forge version to use with it . . . in this case it sounds like you may have the opposite issue, and are using an out dated version of the mod. What is currently running in my pack without any errors is:

Bettermineshafts-forge-1.16.4-2.0.3

Is that the version you have installed?