Overhaul CI pipelines

[adamreichold]

• [x] I agree to follow the project's code of conduct.

• [x] I added an entry to rstar/CHANGELOG.md if knowledge of this change could be valuable to users.

• Bump checkout action

• Avoid unmaintained actions-rs

• Add Rustfmt and Clippy

[urschrei]

bors r+

[bors[bot]]

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• ci result