There are more than 17 Scriptural facts in the Messianic Writings that Y’shua adhered to the traditions of the Jews as prescribed in the Oral Law suggest that.
Sha’ul taught the Oral Law to the lost sheep of the House of Israel with unrestrained effort and even instructed them to obey them:
2 Thess 2:15: So, then, brothers, stand fast and hold the traditions which you were taught, whether by word or by our letter.
Notice that he particularly mentions traditions that were delivered by "word of mouth".
Sha’ul gave severe instructions regarding dealings with people who did not keep the "traditions" or Oral Law:
2 Thess 3:6 But we command you, brothers, in the Name of our Master Y’shua Messiah, that you withdraw from every brother who walks disorderly and not according to the tradition which you received from us.
Sha’ul makes it clear he not only kept the Written Law but the Oral Law as well:
1 Cor 11:1-2: Become imitators of me, as I also am of Messiah (meaning the same as Y’shua did). 2 And I praise you, brothers, that you remember me in every way and keep the traditions as I delivered them to you.
What does Sha’ul say to Believers about those who try to prevent people from observing the traditions of the Jews?:
Rom 16:17: Now I call upon you, brothers, watch out for those who cause divisions and stumbling, contrary to the teaching which you learned, and turn away from them.
Final thought: Whether one accepts it or not, it is a fact attested to by Matthew, Mark, Luke and John, that even in His final hour, Y’shua did not stop practicing the Halachic rites of Orthodox Judaism. Even educational Jewish learning books, such as the Encyclopedia Judaica, say that "the New Testament provides us with undeniable evidence that Yeshua did not oppose any prescription of the Written or Oral Torah."