Hey, just wanted to update.
I tried to make it work for too many hours, but it's one of the elements of Construct that honestly kind of sucks. Sometimes it would be nice for certain options to have more sub-options, where the pin behavior and the drag and drop behavior only let the pinned-to object be dragged as an example (where I would like them to both move and I wouldn't even have had to create this topic). Or a better group possibility.
Instead, tutorials for Jigsaw puzzles that I checked have messy and difficult workaround where variables serve the purpose of grouping together pieces with a common pin object that keeps on being destroyed and created, after which the dragging doesn't look clean either.
It's one of those things that I would like to see managed differently, even more user-friendly like the RPG Maker series in a way.
ANYWAY I'm sidetracking, I simply made a frame for the puzzle and linked the pieces to their appropriate positions instead of linking them to each other. It's not as elegant as I would have wanted but it works. Perhaps in another update I will get back to it!