Assuming a T is open to email contact in the first place, I would never send T updates about my day-to-day living (meaning for ex: "hey I had I fight with my husband and I'm so mad...or I think I need more friends, etc... Those things can wait until the next session.

This is the first T I've had where they said "would you email me what you write about x,y,z). At first I only would contact via email if specifically directed, then we had a trauma session where afterwards I had a huge reaction and sent a brief email saying I was really bothered with T...he responded and we ended up talking on the phone. Another time I felt I just completely flubbed an important question in therapy and once I was home and able to pull my thoughts together, I sent an email thy specifically said "no response needed, just needed to clarify". Mostly, the urge to email stems from trauma work which I do think is fair game however I personally (like you) try and think, "what am I hoping to gain from sending this..is it needing the connection or is there a more specific need?". I love being able to email my T but I am very careful not to abuse it (and in your case, certainly does not sound that way to me). I also try and stay away from weekend emails because I want to respect his personal time.