i'm assuming you don't have access to a house? you can buy an FC room or apartment and use it as storage. or if you do have access to a house and are the owner you can put the furniture into the storeroom. are you keeping around unnecessary equipment for glamor purposes? use the glamor dresser as storage for those.

As for how the inventory system in this game works they can't give crafters/gatherers special inventory bags for stuff. it's the way things are coded. its on you to not keep around things that are not necessary and pare down.