“My” can, but certainly doesn’t always imply ownership. It implies that the qualifier for person B in the sentence is applied to their relationship to me, person A.

My banker, my hairdresser, my dentist, my accountant, my contractor, my neighbor, my boss, my elected official, etc.

Probably not at all on you, here, but this is a good example of “exaggerated progressivism” or fake-woke/politically correct speech. It weakens the credibility of the progressive movement and gives conservatives silly exaggerations to point to and mock, when this kind of stuff emerges.

Just my 2 cents!