How do adherents of sola scriptura respond to “extra” biblical beliefs?

Question

"Extra" in the sense that these beliefs were kept by the Jews but not found in the (39 book) old testament, but nevertheless recorded in the new testament books.

And coming he dwelt in a city called Nazareth: that it might be fulfilled which was said by prophets: That he shall be called a Nazarene. Matthew 2:23

Then Jesus spoke to the multitudes and to his disciples, Saying: The scribes and the Pharisees have sitten on the chair of Moses. Matthew 23:1-2

When Michael the archangel, disputing with the devil, contended about the body of Moses, he durst not bring against him the judgment of railing speech, but said: The Lord command thee. Jude 1:9

Now as Jannes and Mambres resisted Moses, so these also resist the truth, men corrupted in mind, reprobate concerning the faith. 2 Timothy 3:8

Elias was a man passible like unto us: and with prayer he prayed that it might not rain upon the earth, and it rained not for three years and six months. James 5:17

Answer 1

Scripture alone simply means that scripture is the sole rule of all things salvific. It is not about defining the 66 books or more. Nor is it about defining doctrines therefrom. It is only about believing that scripture tells us all we need to know about faith and practice.

In determining doctrine (faith and practice), one looks to scripture alone. We may read other books, consider what early writings reveal, and entertain the thoughts of pious people. What we won't do is say, because Tradition (whatever that is) informs or a Pope pontificates about something, is to say that the something is on par with scripture in terms of being necessary to one's salvation. Of the faith, for scripture alone, ([de fide][2]) is found only in scripture.

So, with that definition and clarification in mind, the fact that scripture identifies things not found previous in said scripture really doesn't say anything and has no bearing on sola scriptura.

They asked John the Baptist are you from God or man? Paul references a poet. In Acts God laid down a sheet for Peter, which was new. The names of Jannes and Mambres weren't written in Exodus, but does knowing them impact doctrine?

The OP idea may be trying to suggest that since there is new information written in the NT that was not in the OT that this somehow supports the idea that other things like Tradition or Bulls not in scripture may have something that is necessary for one's salvation. These things were somehow kept secret from apostles, from eyewitnesses that somehow became necessary centuries later to get to heaven. This is a non sequitur; it doesn't follow. There are all sorts of problems with Tradition, but that's a different question.