I also use android auto a lot. And if i connect the cable to the car before the Bluetooth connection is made , It will remove the Bluetooth pair, It has done this from day one so not part of the Jan update.
Before the January update, my Pixel 6 Pro would randomly connect at widely scattered intervals and only for seconds at a time to my cell provider. After the update, I can connect to cell service, but soon after it drops out. It will only return with a phone restart, starting the cycle again. Am I unique? Is this just a bad phone? Note that my Pixel 3 connected normally in same location.