Four types of Messiah, and Jesus only really fits the 'wise man' type. He's kind of a 'prophet', but not hugely so. He's not really a high priest type, although he does cleanse the temple so that may be an attempt to tick that box. But he wants nothing to do with all the military expectations of a Messiah - the leading of the Jewish nation to independence.
Still a very odd thing for everyone to be so chilled about the guy who makes dead people alive again. You'd think that would get some attention. But obviously not. Curious.
There were a few Jews who claimed to be a Messiah James. Theudas is a good example. Both in what a Messiah would claim and what happened when the Roman military caught up with them.
"It came to pass, while Cuspius Fadus was procurator of Judea, that a certain charlatan, whose name was Theudas, persuaded a great part of the people to take their effects with them, and follow him to the Jordan river; for he told them he was a prophet, and that he would, by his own command, divide the river, and afford them an easy passage over it. Many were deluded by his words. However, Fadus did not permit them to make any advantage of his wild attempt, but sent a troop of horsemen out against them. After falling upon them unexpectedly, they slew many of them, and took many of them alive. They also took Theudas alive, cut off his head, and carried it to Jerusalem. " - Josephus, Antiquities. 20:97-99