Those warehouses only act as access point for other production yards to get materials and to daisychain from other warehouses/collect from producers, they do not supply TO production yards.

Example1:
Your plank maker is in range of a lumberyard > it will to pick up from the lumberyard
Your bed maker is out of range of the plankmaker, but in range of a Construction Warehouse > it will go to pick up from the Warehouse

Example2:
Your lumberyard and plank maker are all the way left of the island (both are out of range of the warehouse)
A Construction Warehouse is in the center of the island (which can cover the whole island)
Your bed maker is all the way right of the island (out of range of everything). This building will not do anything.

The lumberyard supplies the plank maker and the warehouse will collect both excess wood and planks but will NOT deliver planks to the bed maker.

The area range of the production yard in question is the main factor here.

And side note, while we are talking wheels. Some intermediary items have no warehouse allocation like wheels, malt, chipped paper, bronze and other stuff.
Therefore you need to also make sure your cartmaker is indeed in range of the wheelmaker, as the warehouse will not have any in stock ever, though both can get planks at the warehouse on the other hand.

Yeah, I get that, but I have a wagon wheel and wagon manufacturer basically dead center in a populated district that needs lumber and boards. I have both full at a construction warehouse 1 island away. Even with 2 other construction warehouses within range and with wheelbarrows and they WILL NOT go get either of those resources from the other warehouse even though it's over 50% full. The manufacturers ONLY pull from the local woodcutter and plank maker.

Hmm hmm, not quite sure then, once I started running into such issues, started making multiple self sufficient smaller chains scattered around the islands rather than making 1 big hub to distribute.

If your far away storage is filled (I believe the Dev said 33 or 66% filled before others will start to pull from those) and the storages within the dead center area aren't getting anything, then I'm not really sure.
I'm assuming you've been running/observing that for a while and not build too much anymore, meaning the center storage(s) would be mostly capped on all other building materials minus the wood that is supposed to be depleting due to the wheel and cartmaker.

Also assuming you had the place fully/sufficiently staffed so they could keep up with demand in the first place.

In the storage that's not picking up stuff, did you hover over the icons to see what if anything they are actually moving? There is the 15min in/out as well a realtime "+xx" of incoming resources, maybe you can spot something there?

Last Hail Mary would be to simply swap the center storage with any other full storage and see what happens next.

If that still doesn't do it, maybe a screenshot, might spot something.

Warehouses/Markets have a HUGE gathering range, but not the other way around.

If I understand correctly, your producers need to be able to physically walk over to the warehouse to pick up from warehouses and/or drop off to other producers.

So try moving the warehouse within range of the producer.

i feel like the developer could have it so that better roads increase the gathering range since i sometimes have that problem