Several times I’ve read Genesis 16, as I’m sure you have. In this passage, “the angel of the LORD” appears to Hagar. One commenter has suggested that “this special individual spoke as though He were distinct from Yahweh, yet also spoke in the first person as though He were indeed to be identified as Yahweh Himself, with Hagar recognizing that in seeing this Angel, she had seen God (v. 13). Others had the same experience and came to the same conclusion (cf. Gen. 22:11-18; Gen. 31:11-13; Ex. 3:2-5; Num. 22:22-35; Judg. 6:11-23; Judg. 13:2-5; 1 Kin. 19:5-7). The Angel of the Lord, who does not appear after the birth of Christ, is often identified as the pre-incarnate Christ.”
You will, of course, find references in the New Testament to “an angel of the Lord”, but none to “the angel of the Lord”. None of these NT references are equated with divinity as is the angel in the OT passages.
I’d be interested in hearing other thoughts on this.
