CI: Improve caches in rust.yml

[lgingerich]

Is your feature request related to a problem or challenge?

Several jobs in .github/workflows/rust.yml don't attach Swatinem/rust-cache, so they rebuild the workspace dependencies cold on every run. The workflow also maintains a few separate cache keys that all cover roughly the same dependency graph, and at least one dev tool (taplo-cli) is still installed from source on every run.

Describe the solution you'd like

Align cache configuration, check build steps, etc.

Describe alternatives you've considered

N/A

Additional context

Part of #13813

[lgingerich]

take