Update the CI and pin the Rust toolchain version.

[xStrom]

This PR updates the CI to bring it more in sync with the current Linebender standard.

• Various CI action versions were bumped
• The Rust toolchain version is now pinned
• Nightly toolchain jobs were removed
• Docs are now tested with the nightly toolchain
• Snapshots testing is now unified with the main CI for easier config sharing
• Added caching
• Preparation for enabling merge queues

[xStrom]

Alright this PR is now ready for review. 🎉