Isaiah 51: The Lord will save his people in Babylonian captivity

 In Isaiah 51, the prophet talks to those in the captivity of Babylon that pursue what is right and seek the Lord. Perhaps, they shouldn't worship the Babylonian gods. If so, they were mistreated and trying to understand what the Lord is doing. We read:

2
Look to Abraham, your ancestor,
    and to Sarah, from whom you are descended.
    When I called Abraham, he was childless.
    I blessed him and gave him many descendants.
3
So Yahweh will comfort Zion.
    He will comfort all those who live among its ruins.
    He will make its desert like Eden.
    He will make its wilderness like the garden of Yahweh.
        Joy and gladness will be found in it,
            thanksgiving and the sound of singing.

The Lord says that He is saving:

5
My righteousness is near.
    My salvation is on the way.
    I will bring justice to people.
    The coastlands put their hope in me,
        and they wait eagerly for me.

However, what is "salvation" here? I think that it means to get freedom from Babylon:

9
Wake up! Wake up! Clothe yourself with strength, O Yahweh!
    Wake up as you did in days long past, as in generations long ago.
    Didn’t you cut Rahab[a] into pieces and stab the serpent?
10
Didn’t you dry up the sea, the water of the great ocean?
    You made a road in the depths of the sea
        so that the people reclaimed by the Lord
            might pass through it.
11
The people ransomed by Yahweh will return.
    They will come to Zion singing with joy.
        Everlasting happiness will be on their heads as a crown.
            They will be glad and joyful.
                They will have no sorrow or grief.

The Lord asks his people to keep trusting in Him:

12
I alone am the one who comforts you.
    Why, then, are you afraid of mortals, who must die,
    of humans, who are like grass?

14
Chained prisoners will be set free.
    They will not die in prison.
    They will not go without food.

    
Jerusalem is destroyed. Can it revive?

17
Wake up! Wake up!
    Stand up, Jerusalem!
    You drank from the cup in Yahweh’s hand.
        That cup was filled with his anger.
    You drank from the bowl, the cup that makes people stagger,
        and you drained it!

22
Yahweh your Elohim defends his people.

This is what your Adonay says:

I’m taking from your hand the cup that makes people stagger,
    the bowl, the cup of my fury.
        You will never drink from it again.
23
I will put it in the hands of those who made you suffer.
    They said to you, “Lie down so that we can walk over you.”
        So you made your back like the ground
            and like a street for them to cross.    

The Lord will revive Jerusalem and will make Babylon suffer.