The one about Jesus, in Matthew 1:22-23, is a reinterpretation of Isaiah 7:14-17.
Isaiah’s original sign wasn’t even about any messiah, the child to be born, was born at Ahaz & Isaiah’s time, when Judah was at war with the two kings: Pekah of Israel and Rezin of Aram.
The actual sign was about when Assyria would intervene in the war (7:17), and drive out the two kings (7:16), when Immanuel was old enough to honey and cruds, and old enough to know the difference between good and evil (7:15).
So the sign wasn't about Immanuel’s birth (7:14), it was about the rest of the verses - Isaiah 7:15-17.
So Immanuel was no messiah. Immanuel’s role in the sign was only when he reach a specific age, Assyria would come and deliver Judah from the the 2 kings; that’s the actual sign.
Did you know notice that Isaiah started talking on verse 13, but he didn’t stop talking until the end of verse 17, hence the end quote mark.
The sign - the original sign by Isaiah - was never about Mary, never about the “virgin birth”, and never about Jesus being the sign.
The virgin birth and messiah are only the gospel’s incorrect interpretation of Isaiah’s sign. Isaiah’s sign was never about Jesus being a messiah.
Isa 7:14 is about the same child shown in Isa 9. The Jews of course interpret the prophecies to be about the times they were written and indeed they might be but that does not stop a greater fulfilment in Jesus. As a prophecy about God, it would be appropriate to use "virgin" at Isa 7:14 instead of young maid. The word can be used in both ways it seems and the Septuagint translated it as "virgin".
Isa 9:1 Nevertheless, there will be no more gloom for those who were in distress. In the past he humbled the land of Zebulun and the land of Naphtali, but in the future he will honor Galilee of the nations, by the Way of the Sea, beyond the Jordan—
2 The people walking in darkness
have seen a great light;
on those living in the land of deep darkness
a light has dawned.
3 You have enlarged the nation
and increased their joy;
they rejoice before you
as people rejoice at the harvest,
as warriors rejoice
when dividing the plunder.
4 For as in the day of Midian’s defeat,
you have shattered
the yoke that burdens them,
the bar across their shoulders,
the rod of their oppressor.
5 Every warrior’s boot used in battle
and every garment rolled in blood
will be destined for burning,
will be fuel for the fire.
6 For to us a child is born,
to us a son is given,
and the government will be on his shoulders.
And he will be called
Wonderful Counselor, Mighty God,
Everlasting Father, Prince of Peace.
7 Of the greatness of his government and peace
there will be no end.
He will reign on David’s throne
and over his kingdom,
establishing and upholding it
with justice and righteousness
from that time on and forever.
The zeal of the Lord Almighty
will accomplish this.