After further testing, I'm almost certain this is related to the 5GHz band. By changing my home WiFi network to be 5GHz-only, the disconnects happened every minute, with it set to 2.4GHz/6GHz, no disconnects occur.
My guess is the inconsistency we've seen is because if you have an access point broadcasting multiple frequency bands, it'd depend which one you were in as to whether or not you get disconnected.
This would explain why wireless Android Auto always disconnects, because it forces 5GHz. If we also assume that mdapa's university enterprise gear was 5GHz and their old phone hotspot was 2.4GHz then that's also explained.
MAC settings also made no difference to whether I was disconnected or not, the frequency band was the only thing that changed the outcome.