Auto merge of #39728 - eddyb:vendeur-tres-bien, r=alexcrichton

Automate vendoring by invoking cargo-vendor when building src dist tarballs.

This avoids #39633 bringing the `src/vendor` checked into git by #37524, past 200,000 lines of code.

I believe the strategy of having rustbuild run `cargo vendor` during the `dist src` step is sound.

However, the only way to be sure `cargo-vendor` exists is to run `cargo install --force cargo-vendor`, which will recompile it every time (not passing `--force` means you can't tell between "already exists" and "build error"). ~~This is quite suboptimal and I'd like to somehow do it in each `Dockerfile` that would need it.~~

* [ ] Cache `CARGO_HOME` (i.e. `~/.cargo`) between CI runs
  * `bin/cargo-vendor` and the actual caches are the relevant bits
* [x] Do not build `cargo-vendor` all the time
  * ~~Maybe detect `~/.cargo/bin/cargo-vendor` already exists?~~
  * ~~Could also try to build it in a `Dockerfile` but do we have `cargo`/`rustc` there?~~
  * Final solution: check `cargo install --list` for a line starting with `cargo-vendor `

cc @rust-lang/tools