When a PR is ready for integration, the bots add a message starting with "This change now passes all automated pre-integration checks..." and showing what the commit message will be.

This message is updated continuously, e.g. if new reviewers are added.

Unfortunately, the message is only created once the `ready` tag is added, which can be late into the discussion (but then again, still far from the end of the discussion). Finding this message in a PR with lots of discussion is tricky. Sometimes it is even hidden by Github. For an example of a PR where it is hard to fine, see e.g. https://github.com/openjdk/jdk/pull/15138.

I would like to see that this message is added as soon as possible, after the bridgekeeper has done its job. The initial message should just be like:

```
❗ This change is not yet ready to be integrated.

ℹ️ See the **Progress** checklist in the description for automated requirements.

ℹ️ This project also has non-automated pre-integration requirements. Please see the file CONTRIBUTING.md for details.
```

I'd recommend avoiding the author ping until we actually have the PR ready for integration.

Ideally, this should be added even before the label info, if it is possible to control the bot work ordering in such detail. That would make it likely to almost always be the topmost comment, after the bridgekeeper, so it will be clear where to go and look for it.

Since we are already finding and updating the comment, I believe this change would be fairly trivial, and very helpful.