What does good therapy training look like in a training program?
I would say good therapy training includes:
-didactic teaching about psychotherapy theory, which should include case examples;
-ongoing group discussions of psychotherapy theory and practice, which should include group discussions of difficult cases or places where you get stuck;
-doing a sufficient number of supervised cases (ideally 1-2 in PGY2 to get the basics going, and then a significant load in PGY 3-4).
The quality of supervision is absolutely key. If you are getting supervised by someone who doesn't really do therapy you are likely to see your sessions quickly devolve into "supportive" and nonspecific work, the equivalent of chatting about someone's week. You need to have someone who has real experience with therapy overseeing and directing your work, and you need to work in a particular frame (psychodynamic, CBT, DBT, ACT, etc.). You should try out at least a couple of different frames in order to begin to appreciate the strengths, weaknesses, and applications of each.
OP, it sounds like your supervision experience was not great. I think remedying that is the place to start. Find someone good in your community (psychologist or psychiatrist) willing to supervise, and combine self-directed learning with regular oversight of your work. This can be recorded (with patient consent) or discussion-based, your supervisor should be able to guide you.
I very much agree with tr, we should not be teaching ourselves therapy on our patients. Our job is to apply working systems of therapy, not to perform guesswork.