Oh if I'm remembering right, wasn't Belanna's pon farr because of a mind meld?
It seemed to be
male pon farr that rubbed off the overeager Vorik in haphazard touch-telepathy contact. And probably she got just the inconvenient bits of it, rather than the whole deal.
I also don't remember pon farr ever being specifically about sex drive
It was originally about "mating", as the chaste 1960s phrasing went - but the episodes then seemed to emphasize the "finding of mate" interpretation of that word, rather than the "copulate madly" bit. And the more recent bits of evidence don't really bother to contradict that.
No victim of pon farr has ever found relief in lots of sex (even when holodeck attempts at that are suggested in Tuvok's case at least). But nobody has died out of lack of success in murdering, either.
I don't see how just living with Vulcans for a long time would change your biology?
But Spock says it's the price the Vulcan (male)s have to pay for their logic-religion, which isn't biology. And the logic-religion could certainly affect aliens living among Vulcans - through telepathy if not otherwise.
She might've been affected by some of her attitudes, but if I remember right Vulcans are pretty big about arranged marriages, and casually getting together with Ash would suggest she's not really too concerned about that.
Sarek didn't seem to pay much heed to tradition, though. Marrying out of your species might be the thing that Burnham contracted from her foster family first and foremost, even if she didn't quite realize this was what was drawing her towards Ash.
I mean, I feel sort of what you're suggesting would be equivalent to a man growing up around women and somehow developing a menstruation cycle ...
Well, wouldn't he? I mean, insofar as bouts of irrational anger etc. every 27 days or so are concerned.
Timo Saloniemi