[DaltonST]

This has nothing to do with, nor is impacted by, the removal and reinstallation of LC and its .json file.

I reproduced your results, and the Favourites plugin apparently cannot handle your scenario, losing the icon that clearly exists.

Adding the entire LC menu works, of course. Not just a single menu item for LC when the entire LC is also added to Favourites.

Added:
You have added both LC itself, plus a single menu item to Favourites. In my opinion, that is the root cause of your issue. It causes a collision of Favourites unique names. Either do one, or the other, not both, and see if your issue disappears.




DaltonST