Intense crying in session

I just had a really tough session as my client was very upset over a recent breakup. This was very hard on them as we've been working on their anxious attachment and breaking up has always been their worst fear. They spent most of the session sobbing.

I had a natural urge to want to hug her or sit with her but I also questioned a) whether it was appropriate b) if it would be helpful to the client who has been working hard on self soothing and not relying on others and c) if my motives were more to ease my own discomfort versus to support the client.

Anyways, I feel like I kinda froze in my mind and wasn't sure what to do. I tried to be present with the client and validated their emotions but I find I'm playing it over in my mind now questioning how I should have handled it. I worry I came of as cold or uncaring by just kind of sitting their while they sobbed.

I know every situation and client is unique but I'm curious how others handle this in session so maybe I can be better prepared next time to support my client.