here is a link to one explanation of the bar mitzvah
jewfaq.org/barmitz.htm
It says that a ceremony or celebration are not required, but have become something of a custom in modern times.
I was hoping to find a clue to what Jesus might have committed to in a bar mitzvah ceremony, but I don’t see it. Perhaps what Jesus says about having to be in His Father’s house has to do with the essential of becoming resonsible for observance of the commandments and the essential Jewish concept of lifelong study of the Torah.
Aside from what Jesus said, what He was doing was apparently studying the Torah and discussing it.
Mitzvah has the essential meaning of “commandment” but it has the idiomatic sense of “blessing” insofar as when one fulfills a commandment it is a blessing of God and of onself. Honoring His parents is a commandment in which Jesus would have taken great pleasure.