Source for frequent "unstable statuses" errors: PR is ready for merging

### Prerequisites

- [X] I have written a descriptive issue title
- [X] I have searched existing issues to ensure the issue has not already been raised

### Issue

I would not call this a bug report or a feature request; maybe it's just an interesting finding that we could learn from and implement.

I set up a simple repository to try out this action. It basically has lots of dependencies and a `true == true` test suite, so it frequently has dependency updates, and the tests always pass to see the overall behavior.

I often see the `Pull request is in unstable status` error. And I was trying to figure it out. I had required checks, so that was not the issue.

This [issue on another repo](https://github.com/peter-evans/enable-pull-request-automerge/issues/355) mentions that the API will also return this error as "all required checks are already green." So if this action takes longer (I'm running it in an isolated workflow and using auto-merge) than all other checks, it will try to auto-merge and fail because merging is already possible. You can also see this in the UI, as once the PR is ready for merging, the button becomes "merge," not "auto-merge."

One way to reduce this would be to flip approval and auto-merging. If we only approve the PR after we have set auto-merge, it will happen less often as requiring approval is frequently adopted. It won't always fix the issue, but it reduces the chances of it happening. Some food for thought: it's also not a straightforward decision.