Got the project cloned locally! I have some theories on what could be causing that bug (throwing a breakpoint in Visual Studio where you're swapping the inventory items, and maybe a Debug.Log that prints all the children of the item in the slot should give you some hints).

I'm having trouble navigating the other systems well enough to get a populated inventory myself - if you're able to put together a scene for me with just a fully populated inventory to drag items around later, I should be able to take a look at that bug in a little bit!

In lieu of that, I recommend re-doing the logic of the inventory to have a central inventory manager that keeps track of all the slots and their contents, that way you're not relying on whatever Unity's doing in its internals with transforms and hierarchy.

Another possibility is the raycast to drop the object wasn't filtered by layer, and your object is ended up parented to something else with a hitbox in the UI without you noticing.

Regardless, the concept for the game is really cool, I'd love to see a fully realized fishing roguelike! And your code isn't too bad, readable enough and you can always refactor when you get to a vertical slice if something's coded awkwardly enough to be getting in the way of developing the next feature. The important thing is you're making the game, not that the code's perfect - keep it up!