Hmm, Peanut doesn't make exactly the same noise but she'll make a similar one when she's pouting.
When she's upset and throws a half hearted tantrum she'll thrash her head against my fingers making a noise like that and while nipping air with the side of her beak up against fingers. I think it's the Peanut equivalent of "noooo, please stop." She'll also make the same noise if she gets slightly tangled up and feels mildly (but not scarily or in danger) trapped, like she got into a shirt pile and is lost.
It looks a lot like the end of the first clip when she's trying to get free from your hand.
But Birdie's body language is completely different by the end of the video and doesn't match up with Peanut's at all. So it could be that they're using the same noise differently or it isn't the same noise at all. It isn't a sound Peanut makes at any other time.