Tim Sweeny's Epic won their Google Play anti-trust case against Google last year and the 'remedies' are currently being deliberated:
https://xcancel.com/TimSweeneyEpic/status/1812236323815662055
Going through the latest requests by Epic, I cannot find anything about Play Integrity specifically, a massive oversight many others unfortunately tend to make too.
I am not confident there will be another opportunity anytime soon to regulatorily dismantle or, at least, tame the abomination that is Play Integrity in the USA, and whether the EU via the DMA will actually put their foot down on it is speculative, so I strongly suggest that @GrapheneOS reach out to Epic/Tim Sweeny to explain how important it is to focus in on Play Integrity as one of their asks. He is very receptive to the idea of removing dependencies on the Play Store, as evidenced by these tweets:
https://xcancel.com/TimSweeneyEpic/status/1817188838537634044
https://xcancel.com/TimSweeneyEpic/status/1817192476735574333
I do not know how much time is left and while they are still deliberating, I cannot imagine it is very long, so this might be somewhat a matter of urgency. I would also suggest other GrapheneOS users here should tweet at him on this issue, and if (one of) the @GrapheneOS official comments is via tweets, that should be boosted too.