Bring clippy-check up to date with modern APIs

[kristof-mattei]

• Use the integrated way of emitting annotations, removing the need for token, solves this Gitter question
• Fix the issue of duplicated annotations, fixes Action erroniously passing and showing duplicate lints with --all-targets enabled clippy#1 (also an issue here)
• Posts summary with the summary API, closes Use the new GitHub job summaries #164
• Update packages to latest version

[glandium]

FWIW, this works great, but I'll note two things as a bystander:

• Your changes didn't update README.md
• Not sure whether this applies to the original version, because I only tried it briefly and I don't remember how it was, but warning annotations for dependencies from crates.io are showing up on the github actions summary.

[adam-azarchs]

Would be great to merge this, but I'd also note #162

[danieleades]

might be time to fork this repo...

[adam-azarchs]

Looks like @kristof-mattei already did that: https://github.com/actions-rs-plus/clippy-check