If you're already breaking up over text, you probably aren't in a position to worry much about how they interpret your typography. And if they haven't noticed how you normally write there's even less reason to worry about it.
The em dash is just something you can use to diagnose the "AI-ness" of some text, the same way a cough could mean a cold or it could mean something else. You don't need to be self-conscious about it.
Somebody else replied with the video that popularized this bit of insight.
No, it’s not a thing. There’s a new batch of even stupider than normal language prescriptivists that think they’re the first to come up with the concept, though.