Is the passage below a key passage that exemplifies Balzac's intention in writing "Old Goriot" ("Pere Goriot") as a short story?I think Balzac's...

Stately Paris ignores the existence of these faces bleached by moral or physical suffering [reality]; but, then, Paris is in truth an ocean [society] that no line can plumb. You may survey its surface and describe it [society]; but no matter how numerous and painstaking the toilers [literary writers] in this sea, there will always be lonely and unexplored regions in its depths, caverns unknown, flowers and pearls and monsters of the deep overlooked or forgotten by the divers of literature [literary writers]. The Maison Vauquer is one of these curious monstrosities [which now Balzac is exploring in literature].

If your interest is how Balzac approaches his pursuit of the stories in The Human Comedy, then this passage is a key one. It employs a very poetic prose metaphor to compare writing about life in Paris to exploring a vast ocean in which creatures of the deep hide and lurk in geographical crevices that explorers cannot get to. His literary purpose in giving this description and employing this metaphor is the introduction of the principle setting of the story: the Maison Vauquer. It is here that Balzac's characters live and from where their problems and adventures spread.

In terms of your concern with the "relationship shared by reality, which is things as they are, society, which construes reality, and literature, which represents reality," this passage is indeed key. The "faces bleached with physical suffering" certainly describes reality while Paris depicted as an ocean describes society. That Paris needs describing and plumbing confirms that a given society construes how life will be lived there, with some scenarios visible and readily available to description while other scenarios are beyond reach to all but to the most fortunate: "no matter how ... painstaking the toilers." Here, Balzac assumes the role of literature in rendering an accurate and detailed description of society, in all its levels, and the individual "faces bleached with ... suffering" that comprise society.

Thus the relationship, as seen by Balzac, between reality, society and literature is drawn and confirmed in this passage. This may not be Balzac's "intention," as you say, for writing the work--the work may have more particular themes, such as societal corruption--but it certainly presents his intention in writing any given work: his chronicles of Paris describe the reality and society, of all levels, for immortalization in and analysis and (possibly) reform through literature.