Theophylact of Ohrid

After fulfilling everything, they returned to Galilee, to their own city of Nazareth. Bethlehem was also their city, but as a homeland, while Nazareth was their place of residence.

Commentary on Luke ↗

Ancient Greek Expositor

Or again, Luke is here describing the time before the descent to Egypt, for before her purification Joseph had not taken Mary there. But before they went down into Egypt, they were not told by God to go to Nazareth, but as living more freely in their own country, thither of their own accord they went; for since the going up to Bethlehem was for no other reason but the taxing, when that was accomplished they go down to Nazareth.

Catena Aurea by Aquinas ↗

Bede

And when they had completed everything according to the law of the Lord, they returned to Galilee, to their city Nazareth. In this place, Luke omitted what he knew to be sufficiently explained by Matthew, namely that the Lord, after these things, so that he would not be found and killed by Herod, was taken by his parents to Egypt, and after Herod's death, he thus returned to Galilee, and began to inhabit his city Nazareth. …

On the Gospel of Luke ↗

Bonaventure

And when they had performed etc. After Christ's humiliation according to the precept of the Law and his glorification through the testimony of truth have been described, there is here subjoined the last section of this part, in which is described the consummation of the aforesaid things, and this is stated first with respect to the legal precept, then with respect to the prophetic oracle. …

Commentary on Luke, Chapter 2 ↗