Sorry to interrupt, I'll try to answer some of OPs questions.

I have no idea what is involved in supervising students. I also don't know whether my current T ever consults other Ts or is in therapy and so on. But the last T I saw for a while before this told me that usually the whole office gets together once a week and discusses issues from session. Of course they try to make it confidential, but Ts sometimes need input from others, advice on how to handle something and so on. Also, sometimes something a client says will stay with a T in a way it should not (it's their job, they should not think about a client 24/7). In that case they will usually also bring it up in their own therapy.

So they kind of seem to talk about clients, but without identifying the client. Just saying "X causes issues for me, how do I deal with that", or asking for advice for treatment.