Fix deprecation warnings in CI

[danyeaw]

Description

Apologies for the barrage of issues, but I noticed some rough edges while working on #310. 😄

During CI runs we are receiving some deprecation errors:

• Outdated GitHub Actions like actions/cache
• set-output command is deprecated

One of the other deprecation warnings was fixed with #311.

Reproduce

1. View warnings in latest CI run

Expected behavior

No warnings :)