Better question: Why should he be?
There is no shortage of biblical persons that are not mentioned in the Qur'an. Even most of the biblical prophets are not named — or even so much as mentioned — in the Qur'an. You could re-post your exact question hundreds of times swapping only the name of the "missing" person and probably get exactly the same answer. (Please don't do that.)
When someone is mentioned in the Qur'an, it's usually for a reason. This isn't a storybook, regaling us with the history of Jesus. It's a book of guidance, a book to remove doubt, a book to clarify Allah's teachings over false doctrines promoted by people. When someone is mentioned in the Qur'an, it's typically as a teaching tool, using their example to demonstrate some facet of wisdom or faith or piety or… well, whatever. It's a book of guidance which covers all facets of life, so examples are multitude.
26 Indeed, Allah is not timid to present an example - that of a mosquito or what is smaller than it. And those who have believed know that it is the truth from their Lord. But as for those who disbelieve, they say, "What did Allah intend by this as an example?" He misleads many thereby and guides many thereby. And He misleads not except the defiantly disobedient
— Al-Baqarah 26
So why should Saint Joseph be mentioned? His importance to the story of Christ Jesus is one thing, but Christ Jesus was sent to the children of Israel centuries before Muhammad started preaching in Mecca: His ministry is a thing of the past. What story would Joseph bring to the table that would be relevant to the pagan Qur'aysh at the time of Muhammad? What could be taught from his example that wasn't already known to the Christians of the region? Why would the local Jews even care?
And the truth is, I don't know. Allah's wisdom is infinite, I'm sure He could have presented any number of useful stories centered around Joseph. But, again, He could've done the same for any of the hundreds of unnamed persons in the Bible. Or any of the countless generations of humans since creation. Would we have been better off if He had revealed to us an infinitely long Scripture with every conceivable useful example in all of history? Probably not.
The Quran is an Aborgation??? (There is a word people use idk what it is, idk if this is the right one sorry) where it corrects what the precious texts say. Within Christianity, there were multiple views and opinions. Some Christians say Jesus was a messenger (if you look at history you'll know who persecuted thr Jews who believed that 😊, and who protected the Jews from other Christians later in history) and others who believed he was the son of God. While others believed int he trinity. If you look at history, you'll also learn that the companions of Jesus did not agree with Paul. One fo the writers of the bible who dictated the change in Christianity, and they actually questioned him a lot, he wrote like a third of the bible) and Paul does not believe int he narsean trinity. (He has his own understanding of just jesus and the father). You will also see how Jesus explains in John, how son of is a term of endearment (see where jesus talks to the Jews when they talk about the son of God, and jesus explains he is not the literal son). But Paul tries to sell this false idea, despite not actually knowing or meeting Jesus formally in history. Paul also is a document and a self admitting liar.
Where Paul argued if his lies lead others to Christianity, then he is justified in doing so.
So I hope this explains why the Christian perspective is one riddled with issues. And this is excluding the issue of how Christians preserved their message and how weak their preservation is compared to our preservation of the Quran and hadith.
Now onto the discussion about the Quran and stuff around it:
You make claims about the prophet having access to certain books. And certain texts.
If you are being intellectually honest. You should be aware of how the Quran was revealed verse by verse in a different order than the order it was formally given in the last 2 years of revelation. You should also know the Quran is a poetic text that to this day has challenged all humans to make a book like it, and millions of dollars were invested by the 700 club (a Christian group) and they failed to do so.
So to argue it is a book conceived by a man, despite knowing the context of each verse and unexplainable predictions, I'd question that.
This was a bit off topic, but my main reason for asking that question is thsi: Can you prove this man, who is illerate had access to these books, and somehow read them. If so, knowing the sheer amount fo information you have on the prophet, explain when he read these books and how the verses (Quranic verses) revealed around that time have something to do or reflect what he read.
I guarantee you are not looking at the historical context, and geniunely put effort to learn about the prophets life or learn the tafsir of the Quran to understand the context of verses and their time period.
