Coopers Hawk Up By A Nest - Northern Illinois - January 2022

We have a couple of - what we call - "nests" up in some of the larger, mature trees in our backyard.  I say that we 'call them' that because, frankly, we don't know what they are.  They're these large, clumps of leaves that exist up near the top of the trees (in a crotch) that sure look like a nest, but for all I know could just be a clump of leaves that didn't fall down. Or, that was...until I saw something recently up there.  

On a recent afternoon, I saw good-sized hawk swoop across our yard and land right next to one of these nests.  Here, below is a photo showing that hawk perched right on top of said nest. 

Can't quite make out what is going on?  Here, below, is a slightly zoomed in version of the photo:

Still can't quite figure things out?  Here's an even-more zoom'd in version that I've annotated below:

Well....that seems to settle things for me.  A little bit.

This is, most certainly, a nest.  

But, a nest for whom?  

Was the hawk up there because that's where he lives?  

Or was he/she up there because they were looking for a tasty little snack?  And that's actually a squirrel's nest.  Or another critter's nest? 

This page on the US Fish and Wildlife Service's site makes me think we're looking at squirrel nests.  Via FWS.gov comes this screenshot below:

I suppose I should get our binoculars out to have a proper look, but from way down here, that sure seems like a match.  Lots of leaves.  Not a lot of structure.  I'm thinking we have squirrel nests up there.  And that that hawk was, indeed, looking for a little snack.