I really appreciate the work described here, but it seems to me that the performance tests are in exactly the wrong place. The correct time to benchmark a PR is before it is merged; not after. It's the same for any other kind of test; your tests should pass before you merge, not after.
Sure, there will be exceptions where a performance regression is appropriate. But that should be known and agreed on before merging it.
I don't see a strong reason that the performance tests have to be done afterwards. I presume that it's okay to have a delay between creating the pull request and its merge, since humans will typically want to be able to review it!