Grant’s & Sherman’s late war HQ flags have 36 stars. If I’m remembering correctly Ft. Still (museum) has several unissued Artillery Nationals that have 36 stars dating to the CW. They also have about 50 unissued Artillery Regimentals.

I don’t have much on West Virginia (Union) Regiments, Department of West Virginia, but I think they would have carried 36 star Nationals.

The picture you link, looks good to me, a bunting field (service) flag.

Happy Trails!
Tom Martin