"Okay" is extremely hard to purge from one's everyday speech or writing. It's so extremely useful...
Oh, I hate that, too. Dialogue and attitudes that just don't fit with the period.
I threw aside a Regency romance where a duke said "Okay."
And on a similar line, phrases that rely on concepts that the historical background does not support. Someone can't "run out of steam" in a medievaloid fantasy, if steam power hasn't yet been invented!
I too find modern attitudes and viewpoints incongruously transplanted into past eras, exasperating; but re use of language and figures of speech, there's an opposing "take" which I feel has some validity. I personally tend to be more annoyed by extremes of what I think of as "pishery-tushery" or "writing forsoothly" (archaic language, no matter how correct for the period) -- where they are extremes -- than by technically-misplaced modern language or concepts. I value the perspective that overall, human nature has been the same throughout history, and human reactions to the majority of daily life, likewise: I'd rather have characters from past centuries, rendered as talking more or less in the English I'm familiar with from today -- with even a modicum of modern figurative language ("running out of steam", or even "being switched-on") -- than the author knocking themself out to make the characters talk in a, to me, unfamiliar and grotesque manner; or tying themself in knots to find "contemporary" figures of speech. That kind of thing can for me obscure a bit, the characters' being basically humans, with a lot in common with us their descendants -- can give a slight impression that the author is trying to write about aliens.
For me, feeling hit in the face by too-energetic attempts at what described above, can be irritatingly distracting from what's going on in the story. Georgette Heyer always grates on me, just because of the (meticulously researched) Regency slang and idiom in which she makes her characters converse -- I just find it weird and awkward and a distraction: would be more comfortable with "neutral" more modern-type speech. Facetiousness aside -- I feel that though the Regency duke saying "Okay" would have slightly jolted me: I'd have been inclined to give the author a pass for that. It could have been for me more
irritating, and disrupting to flow of story, if the erudite author had had him saying an authentic-for-the-time equivalent. If that were something like, say, "eftsoons", or "I strumple your moggin", I'd have to pause at least a moment to take the new expression on board, and check from the context that it meant basically, "okay" -- I just don't need annoyances like that when reading fiction for fun.