Hello,
instead od AAWireless I use Carsifi adapter, my phone is Pixel 5 with Android 13 and my car-multimedia unit is Navi900. I had diconnecting issues same as Staubsaugermodul, they were completely random, after updating Android 12->13 the frequency of dropouts increased. I tried fiddling with different power saving settings (as mentioned in Reddit forums) and different wifi settings (force 2.4GHz instead of 5GHz, preselect channel instead of autoselect, etc.). However, after last firmware update to Carsifi adapter, all of the problems went away and the connection is stable. Regarding the repeating notification problem, I got this message only after setting up the connection for the first time.