I can see your going round the bend here!!
Im installed on Debian 10 and have the “Supervised” menu as I am running “Home Assistant Supervised”
Try and follow the instructions at Installing Home Assistant Supervised on Debian 10 and you will get a Supervised install and then the ability to restore from snapshots etc. Id recommend the Google Drive snapshot addon too Add-on: Home Assistant Google Drive Backup
I agree that the naming conventions of Hassio, Home Assistant OS, Supervised, etc are all very confusing and I had to search just when posting this to let you know I was running what is called a “Home Assistant Supervised” system. The dev team have tried their best to make things straight forward but it is difficult when reading old posts to know whats what.
The analytics released recently has surprised me that I am only in around 13% of people that run Supervised. I guess when you run a system day in day out you just assume people do the same. https://analytics.home-assistant.io/