I wonder if any of that matters? Optimizing for the things you mentioned feels a bit like overkill. As a non-therapist, I don’t know whether one way of executing therapy is better than another.

I really think it’s simpler than that: find the closest therapist, do an eval session, and see if it fits. If not, try again with next closest. Personal referrals are good too.

You can likely just ask them, but either way I saw their methods plainly advertised when I went looking for an online therapist in early 2021.

Ask them, it's common now for them to advertise their approach (CBT, DBT, psychoanalysis, ect)

psychologytoday's actually a really great place to find these details for local therapists. specialties (trauma, relationships, kids, etc) and likewise training techniques (IFS, CBT, so on). It may have been harder pre-covid but I think covid's shaken up that industry quite a bit.