I assume you mean there might be a self-selection issue with people who are voluntarily ("privately") insured, as compared to those who have the normal state-mandated ("gesetzlich") insurance?

This data is from AOK which is one of the state-mandated insurers. It insures around 2M people, and my gut feeling is that they are not terribly unrepresentative of the workforce as a whole.

But of course the point is, everyone with a tiny bit of true data could tell much more precise stories, and the journalists (as usual) didn't care or didn't think it would fly with readers.

AOK insured 27 million in 2021, couldn't find a more recent number.