Description:
Deprecate/remove cache: gradle option in favor of a first party Gradle action.
If this is not an option, at least mention gradle/actions/setup-gradle in the documentation AND action.yml description.

Justification:
setup-java tries to do too much. gradle/actions/setup-gradle (ex. gradle-build-action) is a fully featured, advanced GitHub Action for caching Gradle builds outputs. It now includes support for things that'll likely never be part of setup-java (e.g. configuration cache caching), leaving users confused and using potentially sub-optimal caching strategies. (example: gradle/gradle#13510 (comment))

Are you willing to submit a PR?
I'll let maintainers handle deprecations / removals, as that's a complex process.