The only difference between the structures of Amylopectin and Glycogen is that Glycogen is more highly branched than Amylopectin. How this difference between their structures makes difference between their solubilities in water?
The answer is relatively simple: Amylopectin is watersoluble, and this seems to be a classical textbook error, which has been propagated now for decades. As you say yourself, the only difference is the number of 1,6-glycosidic branches, which occur every 8-12 glucose monomers in glycogen and every 15-30 monomers in amylopectin.
There are even scientific articles which show that amylopectin is watersoluble, see the references below:
The question is incorrect in asserting that the only difference between amylopectin and glycogen is their extent of branching. This is only an incidental difference.
As I explain in more detail in the answer to another post, the key difference is in the topography of their branching.
This leads to spherical size-limited globules, in the case of glycogen, and large semi-crystalline extended structures, in the case of amylopectin.
This is the basis for their different chemical and physical properties within the cell (glycogen is soluble, starch is in a semi-insoluble form), which is all that is of biological interest to me. I cannot adjudicate on, nor am I concerned with, the properties chemists observe when extracts are manipulated in vitro.