If you drag an added card on a board it originated from to a different column and the boards synced to a sheet and that sheet is set to the kanban setting then when you drag a card on board 1 and it was added to board 2 then both should move to the same column name or place/column number from the left.
I manage many boards that many people place cards into, I add all those cards to my sheet as a to-do list. Clicking around and dragging in both locations is cumbersome. If I go into the card the functionality works by clicking on the linked card link under the title, but drag and drop features are the expected UX. If I change the status since the card is syncing with kanban, then the card should move also.
I feel this would be the best UX for sheets.