Today's test: everything works (connection to the car, S2A remains visible).
Solution:
Set chmod 551 recursively to the folders (just use root explorer and make sure "also include subfolders" is checked):
/data/data/com.google.android.projection.gearhead/shared_prefs
/data/data/com.google.android.projection.gearhead/files/phenotype
Thanks to everyone who went on a "scavenger hunt" with me ... which was unfortunately necessary thanks to our secret bearers.
Not sure why but on my v30 running pixel experience plus I don't have any of that file structure. But like everyone else screen2auto disappears.
I've tried installing aa through nikgapps and also the play store. To try and see if either would create them folders but nope. Also both ways do not create an icon in the app drawer but I can access its settings under app info. So that might be from the rom.
Also on my other phone also a rooted v30 with the stock rom. I have had screen2auto running on it for over a year without any problems.
Update: I decided to try a different rom, crdroid. It has the same file structure in the /data/data folder. But I now at least have an aa icon in the drawer. So lineageOs and pixel based roms don't have (com.google.android.projection.gearhead) in the data/data/ folder
Update 2: Third room was the charm. Installed Evolution X and found the proper files. I knew it was the right stuff when I couldn't change the app shortcuts in the customize launcher settings. So I changed the permission back, adjusted what I wanted then back to 551. So far soo good!
I've been fighting with this for literally months and months. So thank you for your hard work!