A friend who uses Android Auto with TomTom tells me that "My Routes" are available in that system.
Unfortunately - no, i it's not available. I use Android Auto, and that is one of the few disappointments that I experienced with the Android Auto version compared to phone app.
Android Auto also doesn't give us the ability to tap on Route Bar to quickly add Gas Station as Stop Point (and to remove it if we want). We need to go through Search which requires more steps/taps, and it's less safe. Also, we can't report Speed Camera on Android Auto. The mobile app has all of that.
I don't know who and how decide what is safe and what is not, but interacting with phone app on phone mount is interacting with some sort of display, so it is the same as interacting with Car Play or Android Auto screen. But somehow, one is safe and the other is not (!)
I will also like to have ability to create folders/categories for "My Places" and "My Routes". Having one flat structure with a long POI list is bad (from an organizational and safety point of view). And limit to 6 items in Android Auto (Car Play) in order to avoid scrolling is silly, other apps don't have that limitation. A few days ago I saved some location in "My Places" for my next trip. After that, I entered my car, and Android Auto was automatically started, as usual, and I started TomTom Go on Android Auto, I opened My Places to select that POI, but that PIO was not there. Reason? Only 6 items can be in the Android Auto version of the app, and those 6 are alphabetically ordered, so the location that I needed was not there!
For example, the OsmAnd app has access to Routes and to Favorites, and the ability to create (sub)folders/categories, all accessible from Android Auto.