I know that when I am part of observational research or clinical studies, the research group is spending a lot of grant money and funds to do their research on participants, and it seems odd that I'll get paid a stipend from them to going for a visit, them analyzing things like a bunch of bloodwork today, and I get the results. No insurance involved.

If there's something in the bloodwork I don't like, I can chose to see my own doctor or another specialist- then it is up to my insurance to pay.

As to the rest, that gets into the classification of long covid at different insurance carriers. That gets into medical coding and all sorts of red tape that seem related to whether if/how someone is "officially diagnosed" and how the insurance companies take that info. My perspective is that long covid is still relatively new and progress is being made to define it for different entities.