Parrots on the paper doll do not turn their heads when turning the camera

Summary:
When turning the camera in first-person view, parrots on the paper doll do not turn their heads.

Steps to Reproduce:

1. Go to Settings > Video
2. Disable "Hide Paper Doll"
3. Spawn and tame a parrot
4. Have the parrot perch on the player's shoulders
5. Start flying
6. Turn the camera back and forth while looking at the parrot on the paper doll

Observed Results:
The parrot does not turn its head.

Expected Results:
The parrot should turn its head, just like it does when in third-person view.

Video:
Minecraft 2021-12-21 17-42-49.mp4