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lbschenkel @Proxima: before you waste a lot of time doing this experiment, actually try something else first. Open the app properties for MitID and enable the switch named Exploit protection compatibility mode. Make sure to force close the app and try activating again.
I have done that in a new profile and the error no longer showed up for me. Hopefully it will do it for you as well, and then it's good news as we do have a workaround to keep MitID working and they didn't decide (yet) to pull the trigger on Play Integrity.
Can both you and @MentalM try this and report back?