While no “formal” type of address is used, the “Hail Mary” as part of the infancy/childhood narratives in Luke, is composed in a form of Greek that is older than what the rest of Luke is written in.
Luke 1:1-4 is written in Koine Greek–very, very well written Koine Greek. This type of Greek is what is found in the rest of the New Testament, though none of the writers ever show such a mastery over Koine Greek like Luke…except perhaps for the author of the epistle to the Hebrews.
But beginning in Luke 1:5 and through 2:52, the author writes in what is known as Septuagint (LXX) Greek. This was the Greek that was common in the days that the Septuagint was written, the Greek translation of the Hebrew Scriptures.
One could say this is somewhat formal by comparison, but it is really more like what a filmmaker does when shooting a scene in the past in black-and-white format. By doing this Luke is both linking the Gospel with the days of the prophets who were waiting for the arrival of the Messiah and perhaps using this older form as a conduit to render words and expressions spoken to him directly from the Hebrew/Aramaic dialect that the Jews of his day employed.
The oft debated expression in Luke 1:28 where the angel calls Mary “full of grace” instead of by her name is a unique expression in Greek. Because Greek allows for the composition of new words by combining suffixes and prefixes and other parts of words together, Luke does this here. In fact many scholars believe that he is struggling and inventing a new word due to translating an Aramaic expression for which there is no equivalent in any form of Greek.
The infancy narratives end in Luke 2:19, and the boyhood narrative in verse 51, each with an expression found in the Old Testament used to attribute a story to its source. In these cases the source is said to be Mary. It is highly possible that Luke developed these parts of his Gospel from firsthand reports from the Blessed Virgin, and since the story was obviously told to Luke in the Hebrew/Aramaic (perhaps through a translator), the use of Septuagint Greek seemed appropriate.
Contrary to what some believe, the “full of grace” expression in Semitic form is that used when speaking of a vessel that is full of liquid, like water, and had no room for anything more. In the way we talk of petrol or gas tanks as being full and mean we can put nothing more into them, Mary is spoken of as being “filled” with “grace” to the extent that there is no room to add sin into her. The term for “grace” means being gifted or favored with this type of “fullness.”
This logic is foreign to Greek and of course our Western culture. The Septuagint Greek term is trying to grasp this Semitic logic that doesn’t quite translate over, but Luke is gifted enough to use the inflectional aspect of Greek to meet this challenge as best as he can.