As others have said, there's no real way to tell if the t in St represents the first or the second t in Street (or both).
What it means for a letter in a contraction or abbreviation to "represent" a letter in the corresponding full word is not clearly defined for all cases. For example, the abbreviation Rx is used to represent a medical "prescription." The abbreviation does historically come from a word that starts with r (recipe) but that word doesn't contain x either. Furthermore, most people don't know the history, in which case it's impossible for them to have a mental representation of these facts. I don't know how the abbreviation St originates, and there's no reason to suppose that my mental model of how it relates to Street is the same as the one used when it was first established.
Anyway, I have found one relevant non-opinion-based fact that points towards it being taken as representing the last t by at least some writers of British English.
Here it is: some British style guides make a distinction between shortened abbreviations missing letters at the end of the word (which generally are written with a full stop, such as Rev. "Reverend" and Col. "Colonel") and "contractions" that include the last letter, such as Dr "Doctor." (This is described by Barrie England's answer to this question: Does the abbreviation for Saint in a church name require a period?)
In all British punctuation guides that I have found so far that mention St, it is listed as a "contraction" that normatively does not take a final period, whether short for "Saint" or "Street."
This evidence is not definitive because it is not mandatory to use a period even after a shortened abbreviation (some people write Rev for "Reverend") and also, there's no reason to suppose speakers of other varieties of English analyse this contraction in the same way as the speakers who wrote these guides.