Enable cache in CI and locally for ESLint and Prettier

[steverep]

Proposed change

Aiming to speed up CI...

• Turns on caching for ESLint and Prettier in package.json scripts and in precommit hook
• Add cache to CI action using a short-lived key of the commit SHA (will always miss and grab either the latest from the PR or latest from dev branch)
• Adds an action to run when pull requests close to clean up its caches

These caches are small (1M for ESLint and 12K for Prettier) so the cleanup is probably not strictly necessary. But if we add caching for the builds, those would be much bigger and the cleanup makes sense.

Type of change

• Dependency upgrade
• Bugfix (non-breaking change which fixes an issue)
• New feature (thank you!)
• Breaking change (fix/feature causing existing functionality to break)
• Code quality improvements to existing code or addition of tests

Example configuration

Additional information

• This PR fixes or closes issue: fixes #
• This PR is related to issue or discussion:
• Link to documentation pull request:

Checklist

• The code change is tested and works locally.
• There is no commented out code in this PR.
• Tests have been added to verify that the new code works.

If user exposed functionality or configuration variables are added/changed:

• Documentation added/updated for www.home-assistant.io

[steverep]

Closed and reopened to make sure the cleanup action works. Here's the successful run:

https://github.com/home-assistant/frontend/actions/runs/5626915394/job/15248625914

[frenck]

Thanks, @steverep 👍

../Frenck