There are a few times in the Old Testament where the Angel of The Lord seems to be alternating with God speaking, and/or with the Angel saying and promising things we would only expect the Lord to say or promise (of course in Old Testament “Lord” just refers to God), yet after answering as “I” in a Godlike manner, this Angel turns right around and says “The Lord” this and “The Lord” that.
There may be a correlation between when it goes like this and capitalization “Angel of The Lord”, but I’m not certain.
One is Gen 16:7 for ten verses or so. For example: “I” will multiply you. But it was the angel. And calls Him God of seeing. Later she says outright that she spoke to Yahweh. The text always refers to the speaker as the Angel.
Now another example, a big one. The situation at the Burning Bush was such that you literally just asked if God is “standing next to” an angel during the interaction with Moses.
But note: There are other examples. I don’t normally ever post a video link here, but this exact topic was recently covered hereby Rev Winger by Rev. Winger.
Since God is one, there is a way in which the whole triune Godhead was speaking.
Winger ultimately is asking:
Did the second person of the Trinity run around calling himself The Angel of the Lord prior to our Savior arriving in the flesh?