Even though my pets are at 0/10 hunger, they're still showing as "eligible." It even let me battle with one of them (Crinoline against Buttwing Bomber).

However, the pets that are at 0 hunger AND 0 happiness are correctly showing as unable to battle.

Pet that is and should be eligible to battle: Forgotten Realms

Pets that are hungry, but showing up for battle: Crinoline Worldwide Hanbok Madness Hollyberry Tournament Misadventure Frodo Baggins Peregrin Took Exult The Secret Keeper Morenenion Scritches Robin Goodfellow Dead Poets Society Rectify Experimentalality

Ah, okay! Thank you. :)