Just for clarity, I believe the intended meaning of "savantism" in the poem title is not related to "Savant Syndrome" or terms such as "idiot savant" and "autistic savant", concepts that I believe emerged in the field of psychology towards the end of Whitman's life. I think the savantism of the title more likely refers to the cultivation of learning and knowledge, as reflected in th first definition here.
In my interpretation, the poem is about the human endeavor to cultivate knowledge, on the collective and individual scale, and what it says is profound.
The first line hints at how all pieces of knowledge relate to one another, and the "glory" inherent in each act of expanding knowledge (one's own knowledge or humanity's collective knowledge). The second two lines speak of how knowledge and its cultivation underpin all aspects of civilisation - "trades, compacts, establishments", and fifth line talks of how the same underpins all aspects of everyday life - "speech, utensils, politics, persons, estates".
Whitman then connects all this to the field of knowledge that he has personally chosen to devote his life to -- "my leaves and songs", in other words his poetry (which can be considered a type of knowledge). And his attitude towards the task is "trustful, admirant,
As a father, to his father going, takes his children along with him."
In the image of fathers visiting fathers with children in tow, we see Whitman realizing how his lifelong devotion to poetry is merely the pursuit of a type of knowledge by one person among billions over the centuries, and it makes us (me at least) realize that one's own individual endeavors to accumulate that stuff that underpins everthing, and thereby construct one's life, is likewise just one effort among the efforts of billions of the past and future generations. In this way learning and the cultivation of knowledge are like a common link connecting all people through history, and the poem gives a sense of the sacredness of that link.
The image of fathers visiting fathers also speaks to the process of knowledge being handed down through generations and the collective and human aspects of its accumulation.