This is indeed a thing. Anecdotally, when I asked about it on a trans forum, about half the replies indicated that they had experienced some kind of peri-monthly cycle. It is not widely known in medical circles, though I did see that there was one graduate student who was planning to study the phenomenon for a thesis.
My symptoms are now unnoticeable. But for a while, after my GRS, I experienced pain in the surgical area. For the first couple of years,the pain was continuous. But then, I started to notice that there would be pain-free intervals, followed by recurrence. The pain-free intervals seemed to be semi-regular, so, being the nerd that I am, I started keeping track. Yes, the pain wasn't just "semi" regular. It was as regular as clockwork: every 26 days!
When I mentioned it to my doctor, it boggled her mind, too. Like I said, the medical profession does not recognize this as a thing at all.
Anyway, it has been five years now since my surgery, and the pain has finally subsided. With it, my cycle became invisible, since I detected it by the pain.
It kind of makes sense. Hormones are regulated by one of those glands - thyroid or pituitary or something - and everyone has one. It kind of makes sense. Whichever gland it is probably thinks, "Oh, we are running on estrogen now? Fine, estrogen is supposed to go in cycles, so lets fiddle with the breakdown rate to make a cycle."