This is a particular meme that I really don't like. I've used em-dashes routinely for years. Do I need to stop using them because various people assume they're an AI flag?

No, but you should be prepared to have people suspect you are using AI to create your responses.

C'est la vie.

The good news is that it will rectify itself and soon the output will lack even these signals.

Well, I work for myself and people can either judge my work on its own merits or not. Don't care all that much.