It is possible to install Teamviewer as Service on a Host and then connect with the id and password. With AnyDesk i think is this possible too but i'm not completely sure about this because i never read something about running AnyDesk as Service.
This sounds like you're asking for Microsoft Remote Access. Before I retired 2 years ago, I used this every day, with no problems. Microsoft Remote Access for Windows boxes, and HP Remote for Unix boxes.