Woke Pets
Overview
Woke Pets are a new late-game feature added by Lilith. They're untrickable and cannot be used as Batteries, meaning you should not pull Woke Pets before Reso 18 unless required.
Priority for pre-Reso 18 players is exclusively regular pets.
Wishes 
Woke Pets are obtained from a new resource called Wishes, mainly obtained through weekly rewards, which give 8. Pity for Woke Pets is 30 Wishes. You shouldn’t use Wishes until at least level 18 and only when you can afford the breakpoint for the pet you truly want.
Exceptions
Lilith has added certain quests to some events that require using Wishes. If unavoidable, use them to pull any missing Woke Pets first. If you're not missing any, prioritize the current best available pet.
Warning
Do NOT quick ascend Woke Pets if you have Reso 18. Woke Pets do something called Infusion for level 18+, which costs a large amount of bait. The Quick Ascend button automatically performs this Infusion, costing 1k bait. If you’re at Reso 18, manually level your pet to 18 and ignore the Infusion. Infusion is not required for Level 18, it is only required if you plan to go past level 18.