Replace prek GitHub Action with pre-commit.ci GitHub app for better performance #146317

After seeing the discussions in #143148 Replace pre-commit with prek for faster linting and #143149 Replace pre-commit with prek in CI about replacing pre-commit with prek in GitHub Actions, I believe using the the pre-commit.ci GitHub app directly would be significantly faster than both.

The Problem:
Running prek within GitHub Actions is currently slow because it lacks persistent caching. This forces the CI to re-download and reinstall all hooks from scratch on every run.

The Solution:
By switching to the pre-commit.ci GitHub app, we can significantly speed up the process. The app caches environments efficiently, meaning it only spends time executing the hooks rather than downloading and installing them. This would provide much faster feedback on pull requests compared to the current setup.