You noticed it was tagged satire, right? Surely I'm allowed a little leeway. But your point is interesting; there are those who would say converting to Islam breaks the Covenant, and those who would say that if a Messiah is foretold and must be a descendant of David, then he's most likely a Palestinian Muslim whose conversion is a minor issue that Hashem can deal with. (In Isaiah, Cyrus is recognized as a Messiah, and he definitely was no Jew.)

When you speak of Jewish theology, you're talking about a huge, variegated topic, and should at least distinguish between the Holy Torah (law), and later books (prophets, wisdom, etc which bend to it). There's no Messiah in the Torah. That idea comes from various oral traditions, Talmud, & pushed by Maimonides. There is a Kabbalah tradition I've read about where the messiah is descended from Joseph and resurrected by a descendant of David... Anyway, it's not as simple as you suggest.

If Jewish theology interests you, take a look at this when you have 10 mins to kill: https://wiredgourmet.medium.com/when-abraham-ordained-the-god-of-israel-c6ae9356ce35