The example image of a dredging platform shows Chemical Plants feeding each other Ferrous Nodules so I thought I'd do a similar setup for my Cobalt dredging. Unfortunately there is a big issue. When a Chemical Plant has a Cobalt Crust in its output it will not accept any Cobalt Crust for its input. This means that if both Chemical Plants have Cobalt Crust in their output at the same time the setup grinds to a halt as neither can feed the other.

Given the extremely limited space on the dredging platform there is not an easy solution. I am now testing an option where one Chemical Plant feeds itself instead via a series of boxes and Inserters, but to enable that I had to give up my Storage Tank of Sulfuric Acid.

Overall I've found the dredging platform to be a source of endless frustration. For the cobalt setup everything just barely fit even before this issue. Even then it wasn't neat as it required ships that move through each other.

Yeah, it is a tight challenge :)

If you're really struggling, I'd suggest not unloading/loading battery containers on-platform, just shipping in non-containerised batteries. Or you can just have one cobalt processing chem plant (obviously not ideal ratio-wise). Or load cobalt crust directly onto ships and process on land (not the intended solution, but it does work...).

Even then it wasn't neat as it required ships that move through each other.

How many ships are you using for this? You only need 2 or 3 - one tanker for sulphuric acid, and one ship for taking away the containers. The batteries could be in the other ship as well, or perhaps just a small boat rather than a big cargo ship.

I think I have it all working now by having the left Chemical Plant feeding itself while the right plant feeds the left(both are fed by the platform).
The thing that bothers me though is that my original solution was based on the example image and it worked fine for a while until both outputs were occupied at the same time. This was very deceptive as I was sure it had to work because the example used it and it did work for a while.
Also it just FELT wrong as both Chemical Plants had room in their input slots and still neither would export.

To solve the Sulfuric Acid problem I had to add a second ship on that line to make sure there was always a supply.

Regarding the ships I am currently using three ships: Sulfuric Acid Import, Containerized Batteries Import/Export, Containerized Ore Export.
The ships all work fine, but visually they can move through each other at the tip.

I also encountered a strange situation where I ran out of charged batteries for my Discharging Station even though there was a Fast Containerization Machine(FCM) with a container full of charged batteries right next to it. My theory is that the FCM starts unloading too late so it's output slot runs out of batteries before it's done unloading the next container. I've added some accumulators to hopefully bridge the gap.

Both of your problems are related to when inserters decide when to insert into a machine. They won't insert unless the output slots are empty enough.

For the case of the chemical plants, I think this is working as expected, and part of the challenge is ensuring that there's always enough output space. I'm not ruling out changing that though. Going directly from machine to machine is in the example image seems to work ok for ferrous/cupric nodules because they don't return as many relative to how many nodules the recipe takes. But cobalt returns more so it can get stuck.

For the battery machines, it definitely isn't wanted behaviour, and is I believe this bug: https://forums.factorio.com/101436. Really quite annoying with this mod, please post there in support of changing it :)

I was struggling with the same issue where my chemical plants constantly came to a halt. That even happened for my "iron" and "copper" dredges. After a lot of puzzling I managed to add a buffer chest for the nodules from one of the chemical plants. When one of the chem plants is always free of its own excess nodules, the others always have space to drop theirs into each other. The buffer chest gets priority over the inserter taking nodules from the pump. Simple solution, but the challenge was to make it all fit!

I could only fit 2 chemical plants on the Cobalt dredge though, but I think that's normal because of the extra ore. It has the same buffer chest principle going on, so it never backs up either.

A similar situation kept occurring for the battery discharger, where I would find my dredges powerless, and the container-unpacker for the batteries always stuck at a certain percentage. Not sure how that kept happening but I managed to solve that with the same solution as for the chemical plants, by inserting a buffer chest for a certain amount of batteries, enough to guarantee power for quite a while. Again, the main problem was to make it all fit, especially after adding the nodules-chest, but to my own surprise it worked out.

I will return for screenshots, and some blueprints if we can post them here. Hopefully that can help some folks, because frankly, those dredges were a huge pain the butt and constantly having to reboot them almost made me give up on the whole lot. :)

These are some hasty screenshots.

My copper dredge: https://paste.pics/NYKHJ
My cobalt dredge: https://paste.pics/NYKLS
In hindsight the copper dredge could easily do with just one tank of acid, which would have made fitting everything in a LOT easier, but there ya go.

The inserter that is wired to the nodules buffer chest stops working as soon as there's a single nodule in that chest.
The inserter that is wired to the batteries buffer chest puts a certain amount of batteries in that chest. I believe I have set it to 200. (couldn't check).
(Ignore the wires and combinators connected to the ports. They are there for automation with LTN.)

Hope that helps.
Is it allowed to post blueprints, and if so, how do I do that?

Looking at your cobalt dredge I like the overall design, but how does your cobalt packager not get stuck? It seems to output on the same line as its input. Wouldn't that mean you could end up with an input line full of cobalt and no way to output?

Looking at your cobalt dredge I like the overall design, but how does your cobalt packager not get stuck? It seems to output on the same line as its input. Wouldn't that mean you could end up with an input line full of cobalt and no way to output?

It does indeed output on that same line, but a full line only happens when all 4 export-chests are full (as they are in my screenshot), and, well, it kinda makes sense that things come to a grinding halt in that case. :)
The chemical plants have quite long pauzes in between their outputs, which gives the packager more than enough space to place that single container on the belt every once in a while.
I haven't experienced any blockage as long as there's space in the export-chests for the containerized ores.

My first try at building a cobalt platform - https://imgur.com/a/iDJtDjn or https://factorioprints.com/view/-NZuzsrcydXW6RnEKsd9

Basically the original example but a bit tweaked with belt split for cobalt crust - the belt should have enough space to allow output of crust from plants and it would have preference over dredger belt (though it seems it alone cannot saturate 3 chem plants)
Didn't build battery delivery yet, but it should have enough space for it.

Edit: So far it works for me, I supply it with unpacked batteries, with simple load/unload boxes and a discharger, also added 5 solar panels so I won't need to kickstart it if the whole power goes down. The problem left is the logic for battery recharge in port - how many batteries do I need to keep in the loop, how to keep track and replenish them without congesting the belts