Jesus claimed to be the Messiah, that is why he was crucified, we have confirmation of this from outside the bible, just about all critical NT scholars would agree that Jesus claimed to be the Messiah.

Even Bart Ehrman (one of the top NT scholars) who is Atheist agrees that Jesus claimed to be the messiah...

The only real debate is about Jesus claiming to be God.

Different authors will make different claims about the divinity of Jesus and when it started, they would make different claims about who Jesus said he was, but they all agree on a few things (very few)...

They all agree that Jesus was the son of God and they all agree that he is the Messiah.

That being said, the type of Messiah they expected was very different than what they got...

We also have to remember that we have no idea who wrote any of the gospels, but the consensus among critical scholars is that none of the gospel authors ever met Jesus in their life.

Not even Paul met Jesus while he was alive.