Hi Purple!

What I can tell you is that it's an on-going negotiation to keep in touch. Because it hasn't been long since you terminated, I would suggest you keep it short and fairly upbeat. You can mention a struggle, especially one she would be aware of, but mention it in an "I'm still plugging away at X" way rather than in any emotional way. Don't ask for advice, and generally keep it light and simple. It's fine to tell her you miss her, especially with the new term starting, but maybe include her as part of the more general sense of getting used to not being on campus anymore as a new semester begins. I think she will gain confidence in keeping in touch with you the more you control any need you feel to be in touch.

Beyond that, just let time and your feelings and her reactions determine how the relationship continues. I will warn you that it seems common for Ts to respond, but not to initiate. They also seem to not reply to any response you make to their response. So you write, they respond once. They don't seem to continue the correspondence, I suspect because then it becomes a bit murky about how and when the thread ends. And as you've surmised, her response will probably be friendly but short, and it may feel very impersonal at first read. So I wouldn't write until you feel steady enough to not be too invested in her reply.