Add new GitHub Actions job to check that examples compile and are properly formatted

[simongoricar]

This PR adds a new GitHub Actions job called test (examples) to the existing Utoipa build workflow. The job runs alongside the existing test (...) jobs, which means it will run on push or on a PR to master.

It validates all examples in the examples directory by checking that they are properly formatted (with cargo fmt --check) and that they can be compiled (with cargo clippy --all-features --all-targets --workspace --quiet).

I've modified the caching key for the new job so that it will be separate from other jobs, since this cache is likely to be quite large due to several full-fledged web frameworks being included, and I assume downloading it each time would slow down other tests that don't need it.

[simongoricar]

Oops, looks like one example requires nightly and the script fails if nightly isn't already installed (or rather, it doesn't like that the fmt component isn't installed).

[simongoricar]

Alright, the nightly problem is fixed. Fingers crossed that the caching works as well.

[juhaku]

🥇 🏆 Great addition, this really useful and been wanting to have but it has just been in the back burner.