I posed this question to my betterhelp.com therapist. He said..

[I]Yes, I think that it is possible to have a genuine caring relationship with a therapist. However, I suppose it depends on how you define a genuine and caring relationship. A relationship with a therapist will always have boundaries like any professional relationship. Yes, one of these boundaries is that you are paying the therapist to provide a service. As a result, some may consider this relationship to be artificial. I do not find the relationship to be necessarily artificial, but it certainly is distinct from the more organic relationships in our personal lives.

Therapeutic relationships are also one-sided. The focal point is the client and not the therapist. Even when the focal point is the interaction between the client and the therapist, the focus remains on the client, their functioning within this relationship, and how this relates to their functioning outside in the "real world."/I]