Update Post: I sent T a very quick/short e-mail after. I wrote, "T, [outcome of event] Looking forward to our session on Friday. Best, WanderingBark"

I wrote the e-mail before checking this thread again and I wish I had opened with something like others' mentioned for example, "I know we don't usually use e-mail to discuss matters outside of the office, but at the end of last session you requested that I give you an update....etc."

But it seems to have worked out well. He replied, congratulating me on the outcome and said we will discuss it in more detail at next session.

I'm satisfied by his response, but I will ask him if I overstepped and I'll be sure to bring up the process I went through (emotionally and mentally) in writing the e-mail/giving him an update.