Supply lines allow settlements to share junk components for crafting. They also allow sharing of food and water on an "as needed" basis.
Some people mistakenly equated "sharing resources" to mean "sharing workshop storage". This is not how it works. Workshop storage is never shared (except with the other workstations within the same settlement, of course). Only junk/components needed for crafting and food/water are shared on an "as needed" basis. "As needed" means that you draw the necessary supplies from other connected settlements if they are not available in the settlement where you crafting or where settlers need food/water. You do not see the drawn supplies in workshop inventory because they are never there in the first place. They are supplied by the supply line "as needed".