Better Integrate MIR dump in `rustc_mir::util::liveness` into the wider dump infrastructure

Opening this so it doesn't get lost.

In the WG-compiler-nll gitter, @nikomatsakis mentioned that we should possibly update [liveness.rs](https://github.com/rust-lang/rust/blob/ec016f80cf725a9c8a613cdcd2ac97588d5f9af2/src/librustc_mir/util/liveness.rs#L180) so that it uses the infrastructure from #45013.