clusterfuff I'm experiencing exactly the same behaviour since the update.
Jinj Pixel pro 8 with aawireless dongle. No problem until last update.
Recently there have been a bunch of updates, and I suspect there will be more in the near future. So "the update" is arguably not the most productive way to describe what a particular device is running. It is always helpful to provide a build number.
At present 2026062800 is in the alpha-release channel. With luck it will progress to beta and then stable within this week. As expected, that update does contain a change related to Bluetooth and secondary user profiles. It is currently not known whether or not that will help AA in secondary profiles.
Given the existing reports, it is probably not useful to report problems with Android Auto in secondary profiles running on 2026062300. It would be useful to report if the problem persists after a device updates to 2026062800.