Thing is Android Auto only interacts with google blessed devices, iirc device manufacturer has to pay license fee to support android auto. Android auto is not FOSS, I don’t think any automaker would allow their smartphone mirroring to work with rooted hardware that may not comply with safety regulations.
I haven't tried anything advanced with profiles/private spaces yet. But I did successfully get Android Auto to work with sandboxed Play Services and Google Maps just this last week on my "new" GrapheneOS Pixel 9 Pro XL.
