I much prefer “God-bearer” and “Theotokos.”
While I would say that “apostolic tradition” and “[merely or simply] human tradition” do not exhaust the possibilities, I do get fretful at the excessive claims of my co-religionists. I think it's a fine prayer. It's clearly an old prayer. I don't need it to be from the Didache or earlier. And, just as you say, third century ain't apostolic.
My go-to brief Marian prayer is coming up on 200 years old. My favorite longer Marian prayer is not 1k years old. Though I'm grateful for the clarifications and titles of Ephesus and Chalcedon, I haven't based my decision about the intercession of the saints or which prayers I like on their age. I hope you are well.
I prefer *mother of Jesus* because that’s how God, the Holy Spirit, chose to identify her.
If HE thought it was a better term, I don’t have any doubt He would have used it.
But He didn’t.