The standard view of Jesus (Yeshua of Nazareth) is that he claimed up-front to be the literal Son of God. By Islamic standards this is obviously horribly blasphemous, and yet Jesus is still regarded as a major prophet in Islam. How would a Muslim reconcile their faith's hardline divine unicity with a prophet who claimed to be a direct spawn/appendage of God? Or am I wrong about the general historical consensus view of Jesus, i.e. is it thought (by Muslims of anyone else) that Jesus of Nazareth did not in fact personally claim divinity, but rather the divinity of Jesus was strictly a formulation of his followers and later writers?
So the comments here are all talking about whether the historical Jesus claimed to be a descendant of God. Unless I'm misunderstanding your question, the answer to that question is irrelevant. The question is, how did Muslims view this.
Very simply, they (very explicitly) reject that Jesus ever ascribed divinity to himself. The 5th chapter of the Qur'an contains many passages about Jesus. Towards the end, it has these verses:
And [beware the Day] when God will say, "O Jesus, Son of Mary, did you say to the people, 'Take me and my mother as deities besides God?'" He will say, "Exalted are You! It was not for me to say that to which I have no right. If I had said it, You would have known it. You know what is within myself, and I do not know what is within Yourself. Indeed, it is You who is Knower of the unseen. I said not to them except what You commanded me - to worship God, my Lord and your Lord. And I was a witness over them as long as I was among them; but when You took me up, You were the Observer over them, and You are, over all things, Witness.
The Islamic viewpoint is that Jesus never claimed to be anything more than a prophet and that it was later generations who overvenerated him until he became divine. In fact, there's a hadith of Muhammad where he says "‘Do not overpraise me as the Christians have overpraised the Son of Mary. For I am but His slave. So say ‘slave of God, and His messenger’." The point being that "overpraise" of the Christians is deifying Jesus.
Many scholars (Christian and otherwise) think that Jesus did not claim to be the Son of God (also, that phrase has been interpreted in many different ways).
To Muslims, the Bible used by Christians has been corrupted. To Muslims, Jesus didn't claim to be God, The Son, or the Son of God. But he is a law-giving prophet, capable of miracles, and had a divine birth. Also, the Quran says that people only think Jesus was crucified.
Jesus was one of the 4 listed people who were given Holy Books. Jesus was given the Gospel. But this isn't the Gospel that was written by later evangelists. It is a divine revelation, similar to how Moses was given the Torah, and Muhammad was given the Quran.