Okey dokey,
So the good news is, I have had it working on the new phone at least once.
The bad news is, I had exactly the same symptoms as the OP, and it took me an hour to get it going and I don't know what I did to make it work exactly.
The best I can offer before I've gone and had another session with it tomorrow maybe, is to do the following:
On the phone:
Set all permissions fully on for Android Auto.
Set all permissions fully on for Google Maps.
Clear both Data and cache for Android Auto.
Try connecting again. Possibly clear the data again and try a second time if necessary.
I did try a lot of other things including other phones, other cars, bluetooth pairings, other cables and other settings. I suspect they were irrelevant but cant be sure unless I can reproduce the problem.
Given the phone was brand new and had never opened AA before, its very odd if clearing the data is the thing that cured it. Maybe I did things in a different order the first time or chose different options

.
I'd better go for a test drive tomorrow and see if it's properly reliable.