8427: Move CI to rust-cache Action r=matklad a=Swatinem
This is humbling. I actually took inspiration from RAs pre-cache xtask when developing my action ;-)
Closes#7731
Co-authored-by: Arpad Borsos <swatinem@swatinem.de>
This strips the run_clippy implementation out of xtask and replaces it by
a simple "cargo lint" alias which runs clippy with the corresponding flags.
Unfortunately I could not name the alias "clippy" because that would lead to infinite recursion.
