I have a storage controller with a Sophisticated Storage barrel above it with an advanced hopper upgrade in it.
Reference: "System" will refer to my Sophisticated Storage connected chests/barrels.
Good:
If I place any items already in the system in it of any quantity, it inserts the items properly.
If I place any items in a quantity of 4 or less in it that my system does NOT have in it already it will insert into the closest inventory.
Bad/Issue:
If I place any items in a quantity of 5 to 64 that is NOT in the system already the items do NOT move into the system and instead will stay there.

Further to this, if an item stack that is NOT in the system is dragged across the slots to get the quantity lower (see below) it then stacks the first moveable item with the next one and stops.

So this is going to be a bit unpredictable because the barrel with hopper upgrade is also part of the system (automatically added to the system because it touches the controller) so when it tries to insert item into the system the controller basically tries to figure out where the item exists in the system and finds out that it exists in the same "input" barrel and puts it there. So to you it may seem like nothing is happening but in fact the controller inserted the item back into the input barrel.

The reason it worked with 4 is that advanced hopper takes 4 per tick so it takes them from the barrel they are no longer registered in there by controller and thus it tries to put them somewhere else in the system (but somewhere else could end up being in the same barrel as well if there was no space anywhere else or there was no match anywhere else and the barrel was the closest to the controller). And the same thing with the second case.

I know that you're trying to have a drop off storage here that automatically inserts stuff into the rest of the network and I am afraid that's not possible at the moment, but I have a plan to add IO block that servers as another input to/output from the system and based on this I am thinking that block itself shouldn't connect other storages touching it to the system which would allow having drop off storage that pushes items into system. So I will leave this open for that enhancement

Ok, that makes sense. I knew it wasn't a straight up "bug" with how it was acting. I have found combining the "Quickstack" mod with your storage setup works a treat for what it's worth. I do like your idea and I look forward to it. In the mean time. I'll be making another video about the Storage Controller and mention this (temporary?) functionality.
It actually makes sense in a way that if you don't have a place for it in the system, it stays there. Then you need to sort it first and then it will accept it. Basically making a spot for it to fill. I almost would prefer it to not insert at all if it's not in the "system" already. This would ensure that you don't have a pile of individual "food" items going into the closest chest that happens to have "wood" in it (as an example).
EDIT: I did notice that the regular hopper upgrade still is limited to the 4 items like you mention but it actually only takes one item per tick being slower.

Regarding the inserting only those items that already exist in the system that's already possible if you use hopper (vanilla one) or pipes from other mods and pipe items into controller that has locked storages connected to it. In fact it works with individual storages as well - when these are locked they only accept items that already exist in them and so if all storages in the system are locked controller will only put items into storages that already have these and will not accept anything else allowing you to select where those new items are supposed to go.

While that maybe true, the reason I tried this in the first place was because it moves items so much faster than a vanilla hopper. Still, just clicking the controller is the best option I can see.