This PR adjusts the way we cache Cargo dependencies in CI.

We're trying out
[swatinem/rust-cache](https://github.com/swatinem/rust-cache) to see if
it can improve our caching strategy such that we're able to get more
cache hits on PRs.

We'll only write to the cache on `main` in the hopes that it will
mitigate the amount of thrashing of the cache.

Release Notes:

- N/A