i love how you said the part about mikhail as if there are fans of him, lol. thank you for this ask though because i’ve been meaning to sit down and structure my thoughts about their relationship for a while now (assuming that’s what you’re asking about; if you’re wondering about how i came up with the characters in the first place, i’ve been pretty open about them being knock-offs).
to start off, the doctor (viktor) was heavily based on daniil dankovsky and his research of death, but aside from that, as a character he is also inspired by victor frankenstein and viktor from arcane (hence the name), and their united strife to overcome the shortcoming of humanity and reach beyond what is possible. so before becoming the vampire's (olga) lifelong companion, he (late 30s at the time) was similarly overtaken by a desire to study the nature of human life; specifically ways of prolonging it. his research eventually led him to study and be fascinated by vampirism as a phenomenon (much like his other inspiration, edgar swansea from vampyr), which in turn resulted in him becoming a subject of interest not only for the witch-hunting order (inquisition, basically) but also for olga, who is a powerful vampire. she saw great potential in his research and believed it could benefit greatly from her own knowledge of the undeath, so she approached him with an offer of patronage and protection from the order (like how dracula offers the same to frankenstein in the movie van helsing). viktor readily agreed so olga set him up with a lab in the basement of her hidden residence.
viktor is a very direct person; he doesn’t take kindly to being ordered around and talks to people like they are his equals, regardless of whether they have power over him or not. he was obviously very grateful for olga’s patronage but he immediately made it very clear that he considers their arrangement a partnership rather than ownership, and this audacity was precisely the reason olga liked him so much. being a vampire lord, she was used to people and supernatural beings alike groveling at her feet; it was useful to be feared, but it was also incredibly boring. having viktor around not only satisfied her scientific curiosity but also her longing for companionship.
she grew very attached to him (and him to her) in the time that they spent living together, which is why seeing him age with time disturbed her greatly. eventually she offered for him to be turned, but despite his interest in the undeath, viktor refused. instead he proposed for him to feed on her blood in order to become her ghoul (like in vtm). this action inextricably linked them together and made them dependent on each other; according to vampire traditions it also "officially" made viktor olga’s “servant”, but after a decade of being partners neither of them pay heed to the implied power imbalance. hence why they joke around about it.