The notion of a soul is an important conceit throughout Portrait as its one of Stephen's few sustained interests throughout the novel (his two other major, consistent passions are ladies and language, which are all sort of tied together for him anyway). For much of the novel, Stephen thinks of the soul as it relates to mortality and in turn, theology. Naturally, this is a direct response to his Catholic upbringing and the baggage that comes with it (see: Father Arnall's Hell sermon), however, as Stephen begins to revolt against those ideals, he begins to establish new ones that still seem to be based around a belief in the soul.
This brings us back to his two aforementioned passions, with sex and women providing a catharsis for Stephen that carries with it an obvious bridge to the soul (a good reminder of emotional depth that Steven is working with when writing that villanelle). Steven's continued love of language and all of its rhythms and musicality provides a more interesting window into his thinking, however.
If one were to delineate the goals Steven has set for himself in terms of becoming the artist that he wants to become (and I think that's entirely necessary as I see Steven's growth as more artificial than organic), his primary interest is to become what Joyce is: a writer who has managed to divorce human bias from language, creating a landscape of words that elicit pure emotion. This is where soul lies for Steven, however, we as an audience should be wary of the probability of this plan as Joyce himself isn't entirely able to do this, and Steven even less so as we can see in his ode to the unpleasant erotic dream he had.
The big takeaway however, is that Steven's still believes in a form of spirituality, its just been channeled into his art and carnal desires now.