I am not a therapist but have supervised people in academia for >15 years and had quite a few significant mentors and teachers myself when I was young. Some of my most memorable life experiences! From all I know, developing these kinds of feelings is very natural and common in mentor-mentee relationships - I experienced it many times on both ends. I would be surprised to hear if anyone considered them as issues or something to fix... For example, one of my greatest passions in life is learning and having some great mentors were some of the highlights of my life. Likewise, I could be quite annoyed and frustrated if I had to be stuck with incompetent mentors or those that were not a good fit for me. I have seen all these happen in most of my interactions with students as well, including when some come to me to complain and seek help about their bad supervisors or just to tell me how much a good mentor meant to them earlier and even changed their lives.

As far as therapist supervision, I am not a clinician but work in the mental health field and with many clinicians. I attended a few group supervisory classes for Ts out of curiosity (in the US). What I saw was that group members (established Ts or in training) were very much encouraged to explore their feelings of all kinds - in relation to their clients, other members of the group, and the supervisory T as well. When it was something about the supervisory T, the discussion did not usually get into great depth in class but the group leader often encouraged members to set up a private consultation if they felt the need. I know that a few people did that but I never asked them for more detail.

Going back to the one-on-one, I actually think it can be a very good and useful experience to discuss the feelings of the student with the supervisor and I did that myself with both my supervisors and supervisees (again emphasizing I am not a T!) quite a few times. It can help to gain insight into what type of mentoring one likes/dislikes, why, and to keep that lesson in mind when choosing subsequent mentors. The feelings can feel parental but I don't think it always has much to do with our specific parents but it has a lot to do with the scenario of teacher-student. Originally, our first life experiences of learning usually happen in relationships with parents/caregivers and the student-teacher situation is also a learning experience with some hierarchy in it. Personally, I learned tons from exploring my feelings towards my teachers and mentors in my youth and can apply the lessons quite well to developing myself as a mentor, tailoring it to different students' needs. The lessons also help me evaluate better what kinds of students to take on as supervisees. In my experiences, these things can be discussed quite effectively without breaking professional boundaries or ethics, as part of the learning experience. I think it can also be done with an outsider - another professor or therapist. I imagine there may be certain styles/guidelines specific to cultures/countries but I think there is a lot of individual variation as well that specific people apply in their own practice. I guess one can always ask the supervisor whether they would be open to such a more personal conversation?

Again, if I can suggest one thing: don't let anyone make you believe that developing strong feelings toward mentors is a problem that needs to be resolved and lost! They can be used as lessons and tools though.