My feedback has been updated with "Potential fix identified - For a future OS update", so I'm hopeful we'll see a fix in the next beta release.

Following up on my own post. Does anyone know if / how the weekly warnings have changed in Sequoia developer beta 6? After doing a 'tccutil reset All' for my app and re-authorizing it, I haven't seen any follow-up warnings / reminders. So at the very least, the reminders have been fixed so you don't get one immediately after authorizing permissions for an app. Beyond that, I don't know what's changed, or how to reset the warnings so I can test (I'd rather not wait a week). Anyone have any additional info?

I filed this back in April, 2019 (FB5345023). I've found that if I bring the target to the front with NSRunningApplication.activateWithOptions before calling AEDeterminePermissionToAutomateTarget, the hangs don't occur. So that's a workaround, though ugly, depending on your use-case.