What is the best to identify the proper hierarchy of this data?
I don't think your clustering makes sense in the first place. That you actually get some output is more of a coincidence than a result.
Just invoking some functions in a way they don't fail is not enough to get a trustworthy result...

Your matrix is vaguely resembling a similarity matrix, except that it is not symmetric, and the diagonald are not necessarily the maximum values.

Now Ward usually needs a squared Euclidean distance matrix, something very different. The reason why your program doesn't fail supposedly is because it now computes such a distance matrix based on the rows from your similarity matrix. That will usually give somewhat okay looking results (as similar items should have similar rows) but causes subtly problematic bias based on the number of product types.

Later on you can evaluate each hierarchy level based on the agreement with some known label (e.g., manufacturer or product class) and you then can argue which agreement comes earlier. But on a result that isn't valid this doesn't make much sense.