Pretty sure birth control pills are actually progesTIN rather than progesTERONE. Although we sometimes use the terms interchangeably, they are not the same at all, as the progestin will bind to the receptors without actually activating them and thus losing the benefits of progesterone on bone health and more.

A family member doing well on progesterone had nonstop bleeding on progestin birth control. Sorry I cannot recall how long it took to recover when she stopped but I think it took a couple weeks if not closer to a month to get back to her old self.