The Messiah is largely based on Jewish tradition, but there are passages that are accepted by the majority as being messianic. Here is a list I compiled a while ago:
2 Shmuel 7:10-13 (Samuel)
And I will appoint a place for My people, for Israel, and I will plant them, and they will dwell in their own place, and be disturbed no more; and the wicked people shall not continue to afflict them as formerly.
And even from the day that I commanded judges to be over my people Israel; and I will give you rest from all your enemies. And the Lord has told you that the Lord will make for you a house.
When your days are finished and you shall lie with your forefathers, then I will raise up your seed that shall proceed from your body after you, and I will establish his kingdom.
He shall build a house for My name, and I will establish the throne of his kingdom forever.
This has not happened. Wicked people have been murdering Jewish people all throughout history. The Temple is not built. There is no King.
The part that is specifically about the Messiah I have made blue. This Messiah has come and is building a house for God's name by building His Church where God dwells in each member.
He is the King and has established the New Covenant
Jeremiah 31:34 No longer will each man teach his neighbor or his brother, saying, 'Know the LORD,' because they will all know Me, from the least of them to the greatest, declares the LORD. For I will forgive their iniquities and will remember their sins no more."
Jesus is not your King if you are not in the New Covenant and you do not see the Kingdom in your midst.
Yeshayahu 2-4 (Isaiah)
And it shall be at the end of the days, that the mountain of the Lord's house shall be firmly established at the top of the mountains, and it shall be raised above the hills, and all the nations shall stream to it.
And many peoples shall go, and they shall say, "Come, let us go up to the Lord's mount, to the house of the God of Jacob, and let Him teach us of His ways, and we will go in His paths," for out of Zion shall the Torah come forth, and the word of the Lord from Jerusalem.
And he shall judge between the nations and reprove many peoples, and they shall beat their swords into plowshares and their spears into pruning hooks; nation shall not lift the sword against nation, neither shall they learn war anymore.
People still go to war and the Temple has not been re-established.
The Messiah is not mentioned here but the house of the Lord which has been established and is being established and is at the top of the mountains is the Christian Church into which people have and are coming to learn the ways of the God of Jacob.
The Torah and word of the Lord had gone forth from Jerusalem.
It does not say when God will judge between nations and when peace will come however. It certainly does not say straight away when the Messiah comes. How could that be the case if the Messiah has to build the house of God first and the nations are to come into it before that peace happens?
Yeshayahu 11-12-13
And he shall raise a banner to the nations, and he shall gather the lost of Israel, and the scattered ones of Judah he shall gather from the four corners of the earth.
And the envy of Ephraim shall cease, and the adversaries of Judah shall be cut off; Ephraim shall not envy Judah, nor shall Judah vex Ephraim.
The lost tribes have not been gathered back to Israel.
I don't see that this particular quote says that the lost tribes will be gathered back to Israel. But of course that will happen and is happening now as people whose ancestors were part of the last tribes become Christians. (lucky them, they have not been told the same things about Jesus that the current Jews have.) Christians have been attached to Israel and are children of Abraham through faith. The banner is Jesus.
Yeshahyahu 27-12-13
And it shall come to pass on that day, that the Lord shall gather from the flood of the river to the stream of Egypt, and you shall be gathered one by one, O children of Israel.
And it shall come to pass on that day, that a great shofar shall be sounded, and those lost in the land of Assyria and those exiled in the land of Egypt shall come and they shall prostrate themselves before the Lord on the holy mount in Jerusalem.
Not happened yet.
Again the Messiah is not mentioned in that passage.
Yirmiyahu 31:33 (Jeremiah)
And no longer shall one teach his neighbour or [shall] one [teach] his brother, saying, "Know the Lord," for they shall all know Me from their smallest to their greatest, says the Lord, for I will forgive their iniquity and their sin I will no longer remember.
Nothing about needing a middle-man and we don't live in an age where everyone knows G-d is G-d.
What is written above will happen when the full number of the Gentiles have come in and Jesus returns and set up the Kingdom in it's fulness. Our bodies will be changed to spiritual bodies that we will be able to control with out spirits. At the moment we have come to the house of the Lord and are learning the ways of the Lord.
There is an order to events and not everything happens at once.
Yechezkel 37:26-28 (Ezekiel)
And I will form a covenant of peace for them, an everlasting covenant shall be with them; and I will establish them and I will multiply them, and I will place My Sanctuary in their midst forever.
And My dwelling place shall be over them, and I will be to them for a God, and they shall be to Me as a people.
And the nations shall know that I am the Lord, Who sanctifies Israel, when My Sanctuary is in their midst forever.
Temple still not built and the Nations don't all recognise G-d as G-d.
I don't see anything about all the nations recognising God. That will happen eventually however.
Micah 4:1-3
And it shall be at the end of the days, that the mountain of the Lord's house shall be firmly established at the top of the mountains, and it shall be raised above the hills, and peoples shall stream upon it.
And many nations shall go, and they shall say, "Come, let us go up to the Lord's mount and to the house of the God of Jacob, and let Him teach us of His ways, and we will go in His paths," for out of Zion shall the Torah come forth, and the word of the Lord from Jerusalem.
And he shall judge between many peoples and reprove mighty nations afar off; and they shall beat their swords into plowshares, and their spears into pruning hooks; nations shall not lift the sword against nation; neither shall they learn war anymore.
People still go to war. L-rd's House not established.
Same as Isa 2 quote.
Tzefanaiah 3:9-13 (Zefanaiah)
For then I will convert the peoples to a pure language that all of them call in the name of the Lord, to worship Him of one accord.
From the other side of the rivers of Cush, My supplicants, the community of My scattered ones-they shall bring Me an offering.
On that day you shall not be ashamed of all your deeds [with] which you rebelled against Me, for then I will remove from your midst those who rejoice in your pride, and you shall no longer continue to be haughty on My holy mount.
And I will leave over in your midst a humble and poor people, and they shall take shelter in the name of the Lord.
The remnant of Israel shall neither commit injustice nor speak lies; neither shall deceitful speech be found in their mouth, for they shall graze and lie down, with no one to cause them to shudder.
This hasn't happened either. None of it.
Is this meant to happen straight away as soon as Messiah comes. I have already mentioned the Gentiles coming to the house of the Lord and learning God's ways. That is happening. Maybe the Jews will be the last to be converted after the time of the Gentiles is finished.
Zach 14:9-11
And the Lord shall become King over all the earth; on that day shall the Lord be one, and His name one.
The whole earth shall be changed to be like a plain, from the hill of Rimmon in the south of Jerusalem; but it [Jerusalem] will be elevated high and remain in its old place; from the gate of Benjamin to the place of the first gate, until the corner gate, and from the tower of Hananel until the king's wine-cellars.
And they shall dwell therein, and there shall be no more destruction; but Jerusalem shall dwell in safety.
Jerusalem is hardly dwelling in safety and polytheism is still a thing.
So Jesus did not gather the lost tribes, rebuild the temple, not a king etc.
These things will happen also. The temple is being built for the Spirit of God to dwell in and Jesus is King now over a Kingdom you cannot see.
Zech 12 has to happen also and has not happened yet.
Zech 12:1 A prophecy: The word of the Lord concerning Israel.
The Lord, who stretches out the heavens, who lays the foundation of the earth, and who forms the human spirit within a person, declares: 2 “I am going to make Jerusalem a cup that sends all the surrounding peoples reeling. Judah will be besieged as well as Jerusalem. 3 On that day, when all the nations of the earth are gathered against her, I will make Jerusalem an immovable rock for all the nations. All who try to move it will injure themselves. 4 On that day I will strike every horse with panic and its rider with madness,” declares the Lord. “I will keep a watchful eye over Judah, but I will blind all the horses of the nations. 5 Then the clans of Judah will say in their hearts, ‘The people of Jerusalem are strong, because the Lord Almighty is their God.’
6 “On that day I will make the clans of Judah like a firepot in a woodpile, like a flaming torch among sheaves. They will consume all the surrounding peoples right and left, but Jerusalem will remain intact in her place.
7 “The Lord will save the dwellings of Judah first, so that the honor of the house of David and of Jerusalem’s inhabitants may not be greater than that of Judah. 8 On that day the Lord will shield those who live in Jerusalem, so that the feeblest among them will be like David, and the house of David will be like God, like the angel of the Lord going before them. 9 On that day I will set out to destroy all the nations that attack Jerusalem.
10 “And I will pour out on the house of David and the inhabitants of Jerusalem a spirit of grace and supplication. They will look on me, the one they have pierced, and they will mourn for him as one mourns for an only child, and grieve bitterly for him as one grieves for a firstborn son. 11 On that day the weeping in Jerusalem will be as great as the weeping of Hadad Rimmon in the plain of Megiddo. 12 The land will mourn, each clan by itself, with their wives by themselves: the clan of the house of David and their wives, the clan of the house of Nathan and their wives, 13 the clan of the house of Levi and their wives, the clan of Shimei and their wives, 14 and all the rest of the clans and their wives.