Islam isn't based on Christianity or Judasim. Rather is the the revival/continuation of the one message which is monotheism, given to every prophet and messenger throughout history. It would not be unfound for overlap in teachings between the prophets as they are ultimately upon one religion.
While I perhaps agree in principle, I think it's also fair to say that while Islam isn't strictly based on Christianity or Judaism, it was strongly influenced by both, to the extent that the Qu'ran borrows quite a bit from the New Testament, which in turn borrows heavily from the Hebrew Bible. The overlap is not accidental, but rather intentional in order to provide a sense of credibility in their teachings.
In that sense, both Christianity and Islam view themselves as supersessionist to the respective religion that predated them, with Judaism being more or less the root of the Abrahamic tree (though you could argue that Zoroastrianism may have been the precursor for monotheism as a concept, predating them all).
The Qur'an didn't borrow anything, nor was it influenced by the previous religions. The Qur'an is a revelation from God, as was the original Torah to Moses and the Injeel to Jesus. The same accounts of history and messages would be told to the prophets from God.
The claim where Muhammad ﷺ copied from the previous books is simply not possible. An unlettered man narrating and correcting the histories/traditions of the Jews and Christians where they were few and far between in Arabia. It was pagan through and throught. Recounting their history would require a library to be available and be a polyglot in Hebrew/Aramaic/Greek (there were no Arabic Bible translation until the 10th Century).
If the motivation is to gain followers from the prior Abrahamic religions, the easiest thing to do would be to appease their view points and reaffirm what they believed, not to correct them. Not to mention the sheer volume of recounting the children of Israel and history of Jesus in the Qur'an, which does not make sense if you are copying as you would want a few lines here and there to avoid saying something wrong.
(The tone of this comment sounds firm in writing, in reality it is cordial)
This is of course wrong, Mohammed as an illiterate man can copy things because he grew up in a christian and jewish influenced society and no doubt heard the stories of biblical characters and then decided to incorporate them into his own retelling, including various historical errors that make his retelling impossible to be true. https://en.wikipedia.org/wiki/Mary_in_Islam#:~:text=Accordin....
It is also false to say that gaining followers through appeasement is the way to go, there is not a single sect in christianity that doesnt change vital parts of the bible or how to be saved. It is far easier to obfuscate and pretend to follow christianity and then make changes later.
I appreciate your thoughtful reply, and accept it in cordiality! :) And I hope you will accept my replies in the same kindly spirit.
I think perhaps I inadvertently implied that the Qur'an was copied from earlier sacred texts, when I only meant that it was likely influenced by them ... in the same way that the New Testament was strongly influenced by the Hebrew Bible (in some cases referencing portions directly - especially regarding prophetic literature, but in other ways making very different claims). Where I agree with you is that it's simplistic to say that Islam was simply a distant branch of another religion -- it's clearly it's own tradition, but my understanding is that most Muslims would agree that it both shares common roots (i.e. a foundational understanding) with Christianity and Islam while also superseding them.
In my mind at least, that indicates that there is some narrative progression, of which Islam would see itself as the most recent, or most complete, revelation; building on what came before while also correcting it (where it is seen as erring from Allah's/God's intended message). In that sense, I think it shares a lot in common with Christianity, a religion that more or less treats Judaism the same way.
I think there are a great many prophets and messengers throughout history that preached polytheism of one kind or another. There is even one prophet who preached that no gods exist, or at least that they are unimprotsnt to the struggle for a good life - Siddhartha Gautama, the Buddha.