It seems really rude (and slightly cruel) to me that all these Ts are just saying, "OK, see you next week" and then turning away from you to reach for a phone or computer. Is that really what's happening?

My current T stays present with me all the way to the door of her office. She stands up, walks to the door (of her individual office, not the main door to the building), opens the door for me, and usually says something friendly and cheerful ("Have a good week!", "See you next week!", "Drive carefully!" - etc)

If my T just cut me off like that at the end of the time, and literally turned away, that would really bug me. It would make it harder to open up, and feel kind of rejecting. I'm sorry you are all dealing with that.