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According to Ken Dark, this is part of a fourth century "Cave Church." He writes in the online article cited below:
The walls were elaborately decorated with, later-destroyed, multi-colored mosaics, and it was furnished with white marble liturgical fittings. A bench along the west side of its apsidal northern end (an area reached by steps from the south of the cave) contained a series of shallow troughs. These were interconnected so that water could flow through them and out of a glass spout into a channel, leading in turn to a cistern at the north end of the cave. This may suggest that water was dispensed in a liturgical context, probably by clergy to lay people and/or pilgrims.
Along the other side of the cave were at least two rock-cut cisterns, emphasizing the association of the cave with water. Water from one of these cisterns could also be accessed through an aperture in a rock-cut room forming a vestibule to the southeast of the cave. This room led into the cave through a high rock-cut arch, with yet another rock-cut cistern on its south.
While the discovery of a fourth-century and later cave-church is itself interesting, one may also be able to relate this to the description of late fourth-century Nazareth by Egeria, a Western pilgrim. Egeria describes a cave-church in Nazareth, considered by her to be where the Virgin Mary had lived, with a well. Since springs are rare in Nazareth and this is the only known fourth-century cave-church from the city at a site with one, it may be the place mentioned by her.
Dark, Ken. "The Sisters of Nazareth Site." Online, December 2020.
Dark, Ken. “Has Jesus' Nazareth House Been Found?” Biblical Archaeological Review 41, no. 2 (March/April 2015): 54–63, 72.