I did something similar, only even simpler. I downloaded the stub apps to my phone as described here:
When you tap the APK files on your phone, you get a brief message, asking you to allow the APK storage location. In my case, it was the Nextcloud folder on my phone. No need to handle with adb or something like this.
Once you confirm this, you can install all three stubs. Now the Google app, Google Maps, and Google TTS stubs are installed on my phone.
Since Android Auto was already installed on the /E/OS build of my Samsung Galaxy S10, I cleared the cache in the Android Auto app settings, just to be safe.
Then I wirelessly connected my phone to the car, and the Android Auto dialog started on the phone. After going through the process, everything worked as expected. It recognized several pre-installed apps like Phone, Calendar, and a few others, as well as Home Assistant, Here WeGo Navigation, and, for testing purposes, Spotify.
Home Assistant did make some trouble, as it wasn’t not displayed in Android Auto. So I deleted and reinstalled the Home Assistant app. Then I cleared the Android Auto cache again, and everything was fine.
I suspect this was because the Home Assistant App in F-Droid is the minimum version, probably to promote data privacy. But I trust Home Assistant, so I accept the app’s chattiness.
tl;dr
1. Copied the stub app APKs to my phone,
2. Clicked on and installed all three apps (accept APK Source as unknown source),
3. Cleared the Android Auto cache,
4. Optional: Reinstalled the unrecognized Home Assistant app (full version)
I’m totally happy with my ancient Samsung S10 and /e/OS and was totally surprised how easy the switch was.
Finally, all the Big Tech madness is over for me.
I can’t thank anyone enough for making something like this possible.