Auto merge of #110242 - cuviper:vanilla-llvm-16, r=Mark-Simulacrum

ci: add a runner for vanilla LLVM 16

Like #107044, this will let us track compatibility with LLVM 16 going
forward, especially after we eventually upgrade our own to the next.

This also drops `tidy` here and in `x86_64-gnu-llvm-15`, syncing with
that change in #106085.