Here my opinion quickly...
mahdī, (Arabic: “guided one”) in Islamic eschatology, a messianic deliverer who will fill earth with justice and equity, restore true religion, and usher in a short golden age lasting seven, eight, or nine years before the end of the world
1. Jews dont believe Jesus is the messiah, so they are still waiting for one.
2. Jews think the messiah has returned, and appoint him leader.(Think just a person from the line of david, nothing to do with antichrist or messiah)
Yes, that's your opinion, surely, your thinking is from a human perspective, not from GOD's perspective. By your own words, the Islamic eschatology is FAKE, it's a cunningly devised fable and will never fulfill.
See, what we are commenting is about the eschatology based in the Word of GOD, the Holy Scriptures, not in Islamic eschatology wich has nothing to do with the Word of GOD.
Regardings your point 1: Yes, what you said is true; ".Jews dont believe Jesus is the messiah, so they are still waiting for one." Is it written in the Word of GOD? Yes, it is. Even JESUS said:
John 5:v.43-47:
43 I am come in my Father's name,
and ye receive me not: if ANOTHER (a false messiah, AN IMPOSTOR", a CHARLATAN, but the false messiah is also a Jewish Man) shall come in his own name, him ye will receive.
44 How can ye believe, which receive honour one of another, and seek not the honour that cometh from GOD only? (The Word is GOD)
45 Do not think that I will accuse you to the Father: there is one that accuseth you, even Moses, in whom ye trust.
46 For had ye believed Moses, ye would have believed me; for he wrote of me.
47 But if ye believe not his writings, how shall ye believe my words?
Regardings your point 2: No, the Jews will not think the messiah return, but that their hope and belief is fulfilled
when the JEWISH false messiah manifest himself among them. By the way, this MAN already was born and is among them, and at any moment he may manifest himself in Jerusalem, the great city, which spiritually is called Sodom and Egypt-Revelation 11:v.8
2 Thessalonians 2:v.3-4&9-12
3 Let no man deceive you by any means: for that day shall not come, except there come a falling away first, and that MAN of sin be revealed, the SON of perdition;
Who (will) oppose(th) and exalt(eth) himself above all that is called God, or that is worshipped; so that he as God (will) sit(teth) in the temple of God -JERUSALEM-, shewing himself that he is God.
9 Even him, whose coming is after the working of Satan with all power and signs and lying wonders,
10 And with all deceivableness of unrighteousness in them that perish; because they received not the love of the truth, that they might be saved.
11 And for this cause God shall send them strong delusion, that they should believe a lie:
12 That they all might be damned who believed not the truth, but had pleasure in unrighteousness.