It seems the special sound for taking damage from sweet berry bushes is player-specific and other mobs just play their normal hurt sound.
MC-166295
Berry bush damaging sound does not play when other mobs are damaged by sweet berry bushes
Resolved
Invalid
8
(Unassigned)
Confirmed
Low
Sound
1.14.4, 1.15 Pre-release 1, 1.15 Pre-Release 2, 1.15 Pre-release 3, 1.15 Pre-release 4, ..., 20w29a, 20w30a, 1.16.2 Pre-release 1, 1.16.3, 20w45a
Retrieved
Can confirm for Minecraft 1.15 Pre-Release 1