A closed door could change the mini-split versus duct question

For a single-room addition, how much does the existing central system’s capacity and duct layout determine whether extending ducts is a sensible option? A ductless head may avoid opening up walls and ceilings, while a duct extension could keep the room’s heating and cooling less visible. But I’d be wary of assuming the central system can handle the added load without an assessment.

I’m also curious how a closed door affects airflow and temperature consistency with a duct extension, compared with a single-zone mini-split serving just that room. If the mini-split is part of a multi-zone setup instead, does that change the comfort trade-off much?