"Recurring with regularity" is not being a series regular. And whether somebody is a series regular or not is not something that viewers decide.
Ehh... the universe has an objective reality, regardless of fan opinions.
Here's a third season crew picture of the Enterprise. I have a jigsaw puzzle of it.:

During the 1st season, sure, she's a guest star -- she was only in 2 episodes.
In seasons 2 and 3, she was in 23 episodes. Chekov was in 36. Is Chekov a "regular"? Objectively so. And Chapel was in two thirds as many episodes.
She's not M'Benga or Hansen. And she's not Leslie or Hadley either. She's clearly of a piece with the rest of the crew, if the least frequent. Someone has to be.

(now, if you want to discuss what her contract details are vis. a vis. everyone else's, that's also an objective reality, and something @Maurice might be able to she light on...)