OK, I figured out one piece of the puzzle: Catalina automatically switches bluetooth devices when you plug one in.
To turn this on/off you use:
Turning this off I can attach the dongle reliably, but Android still doesn't load it.
sudo nvram bluetoothHostControllerSwitchBehavior=always
sudo nvram bluetoothHostControllerSwitchBehavior=never
I originally purchased this dongle based on a Reddit post (don't laugh) and looking back he was using Android 4.4. Perhaps Android 9 lacks the driver, or has a buggy driver.
It would be nice to try the Apple built-in adapter like I could with the older version of Parallels Desktop, but this doesn't appear to be an option any longer unless I reinstall Yosemite.