I saw a video about your problems related to AI Contributing.

In another video, there was also mention of a proposed solution that GitHub could even have developed.
2 months later, GitHub has still not developed it, and there was a video in recent days suggesting that it might actually be better that GitHub did not develop it.
https://github.com/marketplace/actions/ai-pull-request-equalizer#credits

So I made a very simple GitHub Action:

• If someone has a defined — configurable — permission on GitHub (for example admin/pull), then they can open a PR.
• If someone has at least 1 open Issue assigned to them, they can open a PR.
• If they do not meet either of the above conditions, then they receive a message to channel their energy to a place where there is a shortage of them.

This is a bit different from your current 'Issues are "assigned" or "claimed" by opening a PR' policy.

If you find it useful, then in your current flow I could imagine it as follows:

• Either you allow an always open issue for an external contributor (for example a 'I am not an AI introduction: I would like to contribute to matplotlib' issue)
• Or you switch to the issue assignment mechanism.

(The first requires the least changes compared to the current state.)

Why I think my solution is better than the competing ones:
Simple installation (you only need to copy+paste one file), transparent rules, It redirects AI contributors instead of blocking them — less likely to trigger a strong reaction.

If I have piqued your interest, you can find it here:
https://github.com/marketplace/actions/ai-pull-request-equalizer