Attempting to sink nbt items (Forestry saplings, probably others) to a jabba barrel (also tried TE Caches) results in it thinking the inventory is full (switching to a basic pipe has the saplings go to the barrel and bounce) Providing and requesting does work.
It works as expected on both regular chests and storage Drawers.

I seem to have the same issue with GT6 barrels with saplings and apples.

It has same issues with bees and Filling Cabinets.

Long know issue, still not sure what causes it.

Did a bit of testing, and removing these 2 checks: https://github.com/RS485/LogisticsPipes/blob/dev/common/logisticspipes/proxy/specialinventoryhandler/JABBAInventoryHandler.java#L124-L126
and https://github.com/RS485/LogisticsPipes/blob/dev/common/logisticspipes/proxy/specialinventoryhandler/JABBAInventoryHandler.java#L145-L147
allow sinking to jabba barrels to work properly. I don't know if this the correct fix as I don't know if it's needed for some other reason, but these snippets are the reason it does not work.
E: DSU handler also has this same check.

The reason for those checks was:

At JABBA proxy, you do nothing with doAdd. Is it intended? We add itemstacks to the barrel even if it is not really needed? Smells like an exploit.