The tags are hierarchical to some extent. The question is how specific to make them before relegating detail to some additional key. stone=* is relatively unpopular compared to a more specific material=* value, but that’s partly because few mappers have gone through the trouble of identifying the specific form of stone beyond some well-known generalities.
The reason I said “not to be confused with” is that stone_type=* is completely unrelated to what you’re trying to map. It apparently clarifies the purpose or form factor of a historic=stone, not its composition. Whoever coined this key was at a loss for words, so they went with “type”.