[UCANSEE2]

I’m still trying to figure out what a ‘nest round’ is

That's just how someone talks after several rounds of drinks.

For instance: "Okey-dokey ossifer, what's nest?

[TigersEye]

Officer Wizekreik: “We usually call it a ‘cell’ but since you’re going to be a jailbird you can call it a nest if you like.”