Migrate build system to hatchling (or another non-setuptools option)

[matthewfeickert]

I'd be curious to see a hatchling conversion as a followup (or uv_backend or flit-core). It probably would be faster and simpler. check-sdist might be useful.

I also would like to switch to hatchling (or anything other than setuptools), and while I know it is possible to run custom logic like what exists in setup.py, I haven't done that before, so I figured I would keep this scoped to just pyproject.toml for v0.6.0.

Originally posted by @matthewfeickert in #201 (comment)