

If you’re looking for a medical drama that health care workers seem to find an acceptable representation of their work, take a look at The Pitt. Apparently they put a lot of effort into being as accurate as possible.
Overall I think your definition of edutainment as requiring a narrative is overly restrictive, I think we could call narrative-less science shows like this edutainment, despite lacking narrative:
All that said, the specific combination of scientific accuracy, narrative and for-adults does seem to be a rarer combination of traits. I cannot think of very many at all, and those I can do tend to fudge some of the accuracy here and there for dramatic appeal.









Once you lift the narrative requirement, the number of hits balloons into the millions. I would personally draw the line between education and edutainment on the issue of thoroughness. Education needs to be fairly thorough, while edutainment can skip all the boring (but necessary for full understanding) parts and exclusively handle the fun ideas-based stuff, usually with some oversimplification here and there just to keep things moving in an entertaining way.
I would describe Kings & Generals on youtube as a solid example of good quality military history edutainment.