In general, health insurance companies (at least in the US) are pretty much prevented from using any health data to set premiums. In fact, many US states prevent insurers from charge smokers higher premiums.
It doesn't have to get to your employer, it just has to get to the enormous industry of grey-market data brokers who will supply the information to a third-party who will supply that information to a third-party who perform recruitment-based analytics which your employer (or their contracted recruitment firm) uses. Employers already use demographic data to bias their decisions all the time. If your issue is "There's no way conversations with ChatGPT would escape the interface in the first place," are you... familiar with Web 2.0?
