I believe this is a current limitation of how Monday Docs work inside subitems. At the moment, when you duplicate an item with subitems, the Doc column in the subitems doesn’t carry over its contents — only the structure is copied. That’s why you see different behavior compared to using a Doc column directly on the main item.
It’s not a bug, but rather a product limitation. If having Docs duplicate with subitems is important for your workflow, I’d recommend:
Submitting it as a feature request via the Monday Community or your CSM (if you have one).
As a workaround, you could keep the Doc column on the main item or store the content in a connected item/doc that can be referenced by multiple subitems.
Hopefully Monday will expand Doc functionality in subitems in the future, since you’re not the only one running into this