Fair question, though I’m somewhat surprised you do not know the answer.
Matthew 12:1 At that time Jesus went on the sabbath day through the corn; and his disciples were an hungred, and began to pluck the ears of corn, and to eat.
2 But when the Pharisees saw it, they said unto him, Behold, thy disciples do that which is not lawful to do upon the sabbath day.
Matthew 12:9 And when he was departed thence, he went into their synagogue:
10 And, behold, there was a man which had his hand withered. And they asked him, saying, Is it lawful to heal on the sabbath days? that they might accuse him.
John 5:18 Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God.
Strange you would say this to me right before you would post the same example I'd given you.
Yes, He worked on the Sabbath--generally in service to others. He did so as the Lord of the Sabbath and also as a faithful Jew. He used it as a teaching lesson to those who put man under the yoke of the Sabbath rest in an authoritarian rite rather than allowing men to rejoice in the rest God has given man. The Sabbath was made for man, not man for the Sabbath. This rest wasn't meant to be to the exclusion of the Law given in Deut. 6:3 and Lev. 19:18--and reiterated by Christ in the Synoptic Gospels.
If Jesus transgressed the Law, then He is not an unblemished Lamb for the sacrifice. That He had done no wrong to synagogue or civil authority is noted in Scripture and foundational to His being led to slaughter... not to a just punishment.
When understood this way, you can see that there is good reason for challenging your assertion.