I am happy to inform you the plugin should be working as intended now. I've also included a companion plugin to make the equipped gear be at the top of the list instead of the bottom.
What was wrong
The plugin gives each piece of gear its own private copy so that gems socketed into one sword don't show up in another. That copy gets made when the gear is handed to the party, like from a chest, a shop, or an event.
Starting equipment set in the Actors tab of the Database never gets handed to the party. RPG Maker puts it straight onto the character. So the plugin never made a copy of it, and without a copy there are no real sockets to fill. That's why it didn't show in the socket menu.
The socket circles on the icon still appeared because those are drawn from the note tag, not from the actual sockets. So the gear looked ready when it wasn't.
Taking the item off and putting it back on worked because removing it puts it in the bag, which is finally the moment the plugin made the copy.
What was fixed
The plugin now makes that copy the instant a character is created, so starting equipment is ready from the first frame. Characters who join later in the game are covered too.
It also now handles the Change Equipment event command properly. That command used to put a plain copy on the character while the real socketed one sat unused in the bag.
You shouldn't need to remove and re-equip anything anymore.