I'm from Germany myself. The German health care system has got a lot to offer in terms of therapy, you have to look and search for a little bit, that's for sure... If you check out LGBTI self-help resources you'll find plenty of contacts of LGBTI-friendly therapists.

Yes, 'officially' (on state insurance) you'll ('only') get Behavioral Therapy, or Psychodynamic (TfP), or Analytic Therapy. Which is already a lot more than you might get elsewhere. No systemic approaches are officially covered by insurance. However I've found over the years, that most therapists have done a lot of training in different aspects of therapy and most will work in some sort of "eclectic" style. Or they have added qualifications in somatic experiencing, trauma therapy, imaginative methods etc which will come into the mix as well. It's a question of finding the one that fits for you. And you can try out as many therapists you want, it's covered by insurance.

But I'm also wondering whether your long-time therapist might be right: That you might benefit more from "real" f2f contact. Also, not being an (English) native speaker myself: I've done therapy both in an English and in a German speaking context. The English was fine for current day-to-day problems. Whereas whenever things got to the "core" issues, being in a "different" language "helped" to avoid a lot of emotional stuff which would have been important as a context... Not sure I can bring across, what I'm wanting to point out. I guess, the question is: Whether your insisting on online-therapy and/or having therapy in English might be a way of avoiding what's really important and/or painful?
Just some points to think about.... Might not be the same for you.

Wishing you all the best,
c_r