Cats appear to be floating slightly above the player when sleeping on them in a bed

Cats appear to to float slightly above the player when they are sleeping on top of them in a bed.

Steps to Reproduce:

1. Place a bed
2. Set time to midnight:

   /time set midnight
   

3. Spawn a tamed cat:

   /summon cat ~ ~ ~ {Tame:1b}
   

4. Enter third-person view
5. Sleep in the bed

Expected Result:

The cat would sleep on top of the player.

Observed Behavior:

The cat appears to be floating slightly above the player.

Screenshots/Videos:

Notes:

This is related closely to MC-274420 and MC-272765
(MC-274420 deals with the size of the cat's hitbox, while this issue is entirely related to the model of the entity)