Swap source

If a shot has been worked on already in Fusion from Resolve Fusion Connect, but an updated version of that shot arrives, what's the best way to swap in the new source, and retain all the work already done in Fusion, like Paint fixes?

If you chose to "use the source media," when creating connection, replace the media inside Fusion Composition.
If not, replace the media on a timeline, on the next opening Fusion Composition, it will ask for re-render.
You can check it in Loader node in Fusion Composition: file from cache = second option.

The fastest answer (but surely not the best one) which comes to mind is to create a new Fusion connect and then copy/paste the nodes from the old one...

But as I said, there has to be a more professional way.