So, I just recently learned that fishing ships can drop off food at mills (or any other food drop off building).
However, the behavior is very inconsistent.
The first obvious odd behaviour is that fishing ships will always automatically drop of at the nearest dock, even if a mill is much closer. Only if you delete all docks, will they drop off at the mill.
Second: However, they won’t do it automatically. You have to order a manual drop of at the mill first, before the ship will consider it as an automatic drop off point. This is for standard mills only (as far as I can tell).
Third: You can use landmark/unique buildings as a drop of points (Japanese Farmhouses, Grand Winery, or Japanese Storehouse, Granery) with fishing ships if they are build close to the shore. But fishing ships will never automatically drop off resources at those buildings, even if they are the only availible location. You can only drop off resources manually at them.