Various mobs such as chickens, cows, pigs, and sheep used to panic when receiving poison or wither damage, but now they no longer do.
Mobs that will panic when receiving poison/wither damage:
Elder Guardian
Frog
Goat
Guardian
Villager
Mobs that can panic, but won't due to poison/wither damage:
Baby Piglin
Baby Polar Bear
Chicken
Cow
Donkey
Fox
Glow Squid
Hoglin
Horse
llama
Mooshroom
Mule
Ocelot
Panda
Parrot
Rabbit
Sheep
Skeleton Horse
Squid
Stray Cat
Strider
Trader llama
Turtle
Wandering Trader
Wolf
Zombie Horse
Can confirm in 1.19.1.