Summary:
Mountable mobs do not take damage/regeneration from fireworks and instant potions by the rider. This also applies to parrots that sit on the player.
Since the damage/regeneration from fireworks and potions is given to anyone near the landing/explosion of the projectile, mountable mobs should also take damage.

Steps to reproduce:

1. Taming a mountable mob (e.g. a horse).
2. Mount the mob.
3. Throw an instant potion nearby or shoot a firework to make it explode nearby.

Observed results:
Mountable mobs do not take damage/regeneration from fireworks and instant potions by the rider.

Expected results:
Mountable mobs will take damage/regeneration from fireworks and instant potions by the rider.

Video:
Minecraft Preview 2022-08-08 16-59-20.mp4
Minecraft Preview 2022-08-08 17-00-06.mp4