Use an action `cache` to improve performance about check

[dsherret]

Yeah, caching can lead to a huge performance improvement (ex. https://david.deno.dev/posts/faster-prettier-with-dprint/)

I just did a release of dprint that fixes a caching issue (https://github.com/dprint/dprint/releases/tag/0.41.0) on GH actions. There is a PR here about updating the docs to indicate how to do caching dprint/dprint#740 but building it directly into the action would probably be good. I'm not sure if it should be turned on by default though. I think probably, with a major release of the action.

[NukeManDan]

here is an example of the cache working as expected on update to .dprint.json : https://github.com/Polkadot-Blockchain-Academy/pba-book/actions/runs/6125618243/job/16627953315#step:4:9

Maybe a tiny win, but a win IMHO 😁