I have significantly less experience with pet birds, but the duration and tone of that squawking sounds remarkably similar to a young mocking bird that still has its spots; the spots being an indication that the bird is a juvenile. Typically these juvenile mocking birds can fly short distances, but they only know one song (sqeeek!).
Juvenile Mocking Bird
https://www.youtube.com/watch?v=pDldUhCOJkQIf you observe a juvenile mockingbird long enough you'll note that one or more adults are near by (usually parents) guarding and often feeding these young birds. Even though these birds will eat what they can on their own (you'll often see young mocking birds do a multi-stepped wing opening to flush insects out of the grass), their hunting/foraging instincts are not completely sufficient yet to feed them on a daily basis.
The point is, for a bird that can live at least 30-40 or more years, this one is very much so still a juvenile. From the second video it still seems rather afraid of you (staying in the cage), but will none the less tell you it's hungry (squawking and climbing higher).
To illustrate what I mean by this:
In addition to squawking for attention, when my birds demand either mine or my wife's attention for one reason or another they'll either dance at the very edge of the perch on top of their cage until they almost fall off (I think this is an unsureness about flight) or if they really want what we have (like an apple) they'll fly to us (which they do more and more often).