On the one hand, employers shouldn't discriminate against people struggling in any way with mental health, and contact with a T should be seen in just the same way as contact with any other healthcare provider.

On the other hand this is sadly often not the case, in society generally as well as in the workplace. So my advice would be not to speak about seeing T when you first arrive.

If it was a permenent job, you could spend time getting to know your colleagues and the workplace culture, and figuring out whether you would want to share something like that. Honestly in an internship I would advise simply not to share.

I have occasionally had a break from regular sessions due to work commitments. I think I always found it is easier if you are the one going away and doing something different, rather than it being T who is gone. I think the phone check-ins are a great idea. For me that has always helped a lot.