Assign a ghoul or one of the robots from Graygarden for the supply line. Your provisioners might be dying from irradiation in the ocean.
The items don't actually show in the workshop, but they are there.
If you try to build something, you'll still be able to build as long as the connected settlement has the stuff.
That may not be the case here. I think OP is referring to not having crafting supplies. I may be wrong.
The supply lines to Spectacle Island are kind of patchy in my experience. They seem to cut out a lot and just disappear altogether on occasion. This seems to be remedied by outfitting the provisioner with a hazmat suit, or alternatively assigning a ghoul or one of the Mr. Handy's from Goodneighbor to that supply line.
I'm going on the 'none of my gear appears at the workshop' part.
But yeah, assigning a normal settler to the supply route for the island doesn't work well either.
Yes, I know, but I'm getting the impression that this was just poor wording. At least that's what I'm taking from the "not going to manually carry my crafting -gear- to the island" part of the post.
Some clarification would be helpful here in either case.
As a side note. I have had this happen. The supply line is intact and then all of a sudden, nothing. I was even in the middle of building things and then I couldn't build anything anymore as I had no supplies. Look at the supply line in the map and the is no line there. I have the route set to the castle. If I fast travel to the castle, the supply line returns and all is well. This has happened numerous times. The settler is not dying as I have never assigned anyone but him to it.
One thing I found fast traveling to the castle was that same settler there using the weapon crafting bench, once I pushed him aside the supply line returned. Its like they get distracted, but only this one.