Hello, I started out the same way (I'm only a month in) with a separate user profile for Android auto. I was able to get Android auto to work. Wired. I can't see the Imgur screenshots, not coming up. Hard to help, sorry. Good luck if you can keep this up, I hope you can. This might not be the best advise, but maybe delete the user profile and start again and focus on the permissions again. When I was having issues with Android auto, I went into Apps, Sandboxed Google Play, and sat in my car and played with the permissions in Play services section & Android auto section, until I got things to work.
Following, please feel free to ignore, but this was my experience, and what I eventually did.....
Unfortunately, Android auto, although usable, was hard to use for me in a separate profile. If you get a Signal message from the main profile while driving, unless you pick up your phone, change users, input your fingerprint and then secondary PIN, look at the message, forget it. So the people I convinced to use signal now used sms because I wouldn't answer during my commutes! Yeah, you can have another signal account, Molly, etc... But try to convince other non-GOS users to work with you on that when they are already losing patience.... Depends on how much inconvenience you can handle.
Eventually I kept non google apps in Owner profile without Play services, and deleted the 2nd user profile, and put Play services in the Private space. I had Android auto in private space. It was better, but could not get Android auto full functionality. Mainly hands free was issue. Driving with kids in car watching you asking why you are touching your phone when driving and not using hands free anymore.... Not safe. I hope to replace this with a more private way to do hands free in the future that works with android auto if that ever is available.
So, I eventually went to all apps in Owner profile, including Andoid Auto and kept Private space for perhaps finance. Finally works well. Felt really DIRTY in beginning to mix...... Especially since I had to install Google assistant to get Android auto hands free and give Play services more permissions.... A lot of tinkering. Ugh.. But it works really well. Hands free functionality is perfect! Better than my old Samsung phone which used to disconnect from Android Auto. RCS messaging also works flawlessly.
I don't have a lot of apps from Google or Google play store, but I do. I try to start with Accrescent first. Then Obtanium and get app from GitHub after doing a lot of research to make sure I trust it as much as is feasible. Then Google Play store. I continuously try to find open source alternatives that I trust and replace the Play version, but that will take time... It's ok. Some on this forum poo poo use of google play services, but Graphene Devs don't endorse that, clearly they spent a lot of time making sandboxed Google Play services and giving you the freedom to choose how you want to set it up. Overall, it's not ideal, but markedly better then going to back to Samsung or Apple! I'm loving GOS.
Oh, and perhaps give Tom Tom maps a try. Only one I've used that is as accurate as Google Maps for navigation. Traffic is decent. No distractions from all the stuff on the screen (objects, car stopped etc), but you won't get police warning, so cruise control 9 mph above limit and you're fine. The others were not as good at navigation (OsmAnd, CoMaps), some sent me way off course.
All the best