Always install Rust and use `Leafwing-Studios/cargo-cache`

[BD103]

This PR has two parts:

1. Some jobs don't actually install Rust before using it. This doesn't error because Github's hosted runners come pre-installed with Rust, though it is frequently outdated.
2. Use Leafwing-Studios/cargo-cache for all jobs that use Rust. This action is wonderful: I've been using it successfully for a month or so now. (Also it's by our friends at Leafwing, so it can be trusted!) This should speed up many jobs without the usual tradeoffs of caching.

[BD103]

I'm marking this as contentious because it is pulling in an outside dependency, but I feel like it's from a trusted source. If this gets major pushback, we can fork Leafwing-Studios/cargo-cache under the Bevy organization and frequently update it.

[BD103]

I'm rebasing this on top of #1403 so CI passes. Consider this blocked until that PR is merged.

[rparrett]

Just linking in discussion from the twin PR for the bevy repo. https://github.com/bevyengine/bevy/pull/13040

[alice-i-cecile]

Yeah no objection to handing off ownership to the Bevy org if this appeals to y'all :)

[BD103]

@mockersf what are your thoughts on merging this? It would provide a good testing ground for introducing this action to the main Bevy repository, and Alice even offered transferring the repository.

[janhohenheim]

Note that cargo-cache is about to release v2: https://github.com/Leafwing-Studios/cargo-cache/pull/17

[BD103]

Let me enable the sweep-cache option before this gets merged :)

[BD103]

Hah! Turns out this found a bug with cargo-sweep: https://github.com/BD103/cargo-sweep/issues/7. Let me fix that real quick...

[BD103]

I'm going to close this. I no longer have the time / energy to work on it, though anyone else is free to pick it up!

I'll create an issue for this, though, so it's not lost.