I've had seven piano teachers, if I'm counting correctly. Some good, some not so good, one very good, at least for a few years. I've never had the kind of close, intimate relationship with a teacher that you describe. I love the music; I want them to teach me things that will help me play better, but learning to play is entirely on me. If they help, that's terrific, and they often do. I guess I have somewhat limited expectations from a teacher - I want them to remind me of things I keep forgetting until I don't forget anymore (e.g. "shape the phrase with your arm not your fingers"), I want them to give me ideas I had not thought of myself about how to practice difficult passages, and, more so in the past than now, I wanted them to point me towards repertoire that was at the right level of challenge. I had one teacher who thought it her job to fix things she thought needed fixing about my outlook on the world or my personality, and after a while that kind of boundary crashing outweighed the good stuff she was teaching. If I wanted a therapist, I'd hire someone who was actually trained in that. And to be fair to her, she was excellent with students who had suffered some kind of musical trauma in their youth, but it was not what I needed - she had a hammer, but I wasn't a nail. A good thing about having had a bunch of teachers is that they have different skills and strengths and outlooks, so by having a bunch over many years you get a wide range of ideas.
If you are interested in reading about a bunch of piano teachers, the excellent (in my view anyway) concert pianist, Jeremy Denk, has written a beautiful memoir about all of his teachers called Every Good Boy Does Fine, which you might find interesting. You can also get an idea about what various teachers are like just by looking at youtube - Josh Wright, Graham Fitch, Nahre Sol, Danae Dorken, and John Mortensen, are all very good teachers with different styles; watching some of their videos might help you think about what you need in a teacher.
Good Luck.