When considering the whole rupture-repair idea, I personally would first ask myself what I intend to use my therapy for primarily. I am saying this because I did not consider it well enough in the past. What happened was that my original, primary (practical, outside of therapy) goals sometimes got diluted or lost in focusing too much on what was going on with my therapist. I even used it as a distraction to not deal with my real issues properly. So, what I would try to measure is how much mental energy and therapy time is worth spending on discussing conflicts and feelings around it with the T. (I prefer expressing it resolving conflicts, "rupture-repair" is a therapy buzz term that sounds overly dramatic to me.)

For me, when things like that happened around emailing, I discussed it with the Ts very directly. I knew from start that I had an issue with excessive virtual communication and I very much expected it to show up in therapy as well. It did, it wasn't specific to the therapist at all but a general distraction pattern that I would apply to many different people and situations. The way I handled it in therapy: I shared this with the Ts and asked them not to reinforce my habit even if I seem uncomfortable or get frustrated.I also liked to remind myself that I was paying the T for session time and not for engaging with me when I wanted, between sessions. I would see wanting them to respond to every email (or even to respond at all) without extra cost as an unrealistic and even unfair expectation. If they offer it, fine and it's a sort of luxury, but I would not feel I have the right to demand that service for free. I know this may sound a bit too rational, but it did help me keep my impulses and expectations in check.