They usually call that a rider — or more specifically, a tour rider / hospitality rider when it includes green room snacks and other backstage requests.

What it means

A rider is the list of conditions attached to a performance contract, covering things like food, drinks, dressing room setup, and other backstage needs.

Common slang

When people talk about especially odd or flashy requests, they often call them diva demands or backstage demands.

Simple example

So if a musician asks for specific snacks, fruit, bottled water, or weird decor in the green room, that’s usually just part of their rider.

TL;DR: the term you’re looking for is rider.