I've wondered what type she could be. I think she VIs as a Gamma SF. I would have even seriously considered ESI. But from her songs (and she actually writes her own songs, so that's convenient), I would type her as IEI (also from her interviews).

I think she's a "sincere" IXFx type, because she writes a lot of personal things, and there's a sort of emotional sincerity to it

Not the "passionate" EXFx.

I think she's a Positivist Ni. A lot of her later songs are quite vague and metaphorical. Most of her songs are quite cheerful and positive. EIEs tend to have more "ironically happy" songs, like "I'm really sad, but I'm making it happy for you!".

This is the kind of image that she seems to want to portray from her songs:

Oh, your sweet disposition and my wide-eyed gaze.

'Cause it reminds you of innocence and it smells like me

Well maybe it’s me
And my blind optimism to blame

Laughing at the other girls who think they're so cool
We'll be out of here as soon as we can
She is "wide-eyed", "innocent" and "blindly optimistic". I don't see how that can't be IEI.

This is Ni, seeing historical patterns:

And it’s a sad picture,
The final blow hits you
Somebody else gets what you wanted again
And you know it’s all the same,
Another time and place
Repeating history and you’re getting sick of it
Positivist Ni, seeing things change for the better:

Because these things will change
Can you feel it now?
These walls that they put up to hold us back will fall down
This revolution, the time will come
For us to finally win
And we’ll sing hallelujah, we’ll sing hallelujah
This is obviously vaguely Beta:

So we’ve been outnumbered
Raided and now cornered
It’s hard to fight when the fight ain’t fair
We’re getting stronger now
Find things they never found
They might be bigger
But we’re faster and never scared

You can walk away, say we don’t need this
But there’s something in your eyes says we can beat this

Tonight we'll stand, get off our knees
Fight for what we’ve worked for all these years
And the battle was long, it’s the fight of our lives
But we’ll stand up champions tonight
"Casually cruel in the name of being honest"? Sounds like a difference between Fe and Te values...:

Hey, you call me up again just to break me like a promise.
So casually cruel in the name of being honest.
I'm a crumpled up piece of paper lying here
'Cause I remember it all, all, all... too well.
Lots of vague and metaphorical Ni lyrics:

I remember
You took a Polaroid of us
Then discovered (then discovered)
The rest of the world was black and white
But we were in screaming color
And I remember thinking…

Are we out of the woods yet?
Are we out of the woods yet?
Are we out of the woods yet?
Are we out of the woods?
Are we in the clear yet?
Are we in the clear yet?
Are we in the clear yet?
In the clear yet?
Good

When the flowers that we'd grown together died of thirst
You're still all over me like a wine-stained dress I can't wear anymore

Hung my head as I lost the war, and the sky turned black like a perfect storm

There was nothing left to do
When the butterflies turned to dust that covered my whole room
So I punched a hole in the roof
Let the flood carry away all my pictures of you

The water filled my lungs, I screamed so loud but no one heard a thing

Loving him is like driving a new Maserati down a dead-end street
Faster than the wind, passionate as sin, ending so suddenly
Loving him is like trying to change your mind once you're already flying through the free fall
Like the colors in autumn, so bright just before they lose it all

Oh, losing him was blue like I'd never known
Missing him was dark grey all alone
Forgetting him was like trying to know somebody you never met
'Cause loving him was red
Yeah, yeah, red
We're burning red