Good point there about in the "real world". And that's encouraging. Perhaps it's because most people instinctively know it's offensive. As I said, the medical community seems to have gone with pregnant person. I don't know of many outside the far right who have a problem with that, as you are indeed a pregnant person.
That said, "birthing person" has been pushed in media and commentary. It's also been picked up by misogynists and used, again mostly online.
Which means that it will filter down to "real life". Not a single one of us is aware of every single conversation that happens in the real world, across our respective countries or across the world.
I don't hear it ubiquitously. I have heard it, in the context of discussing the term.
One thing is clear to me, media has the power to normalize things, for good or for bad. Seeing the term so prevalent in the media in the way it has been is concerning.