The em dash usage conundrum is likely temporary. If I were you, I’d continue using them however you previously used them and someday soon, you’ll be ignored the same way everybody else is once AI mimics innumerable punctuation and grammatical patterns.
If they wanted to watermark (I always felt it is irresponsible not to, if someone wants to circumvent it that's on them) - they could use strategically placed whitespace characters like zero-width spaces, maybe spelling something out in Morse code the way genius.com did to catch google crawling lyric (I believe in that case it was left and right handed aposterofes)
Just replace them with a single "-" or a double "--". That's what many people do in casual writing, even if there are prescriptive theories of grammar that call this incorrect.
I suspect it's a spandrel of some other feature of their training. Presumably em dashes occur disproportionately often in high-quality human-written text, so training LLMs to imitate high-quality human-written text instead of random IRC logs and 4chan trolls results in them also imitating high-quality typography.
