Mounting horses, donkeys, mules, zombie horses, skeleton horses, and camels no longer forces you to face forward

Before 24w36a, mounting horses, donkeys, mules, zombie horses, skeleton horses, and camels changed the direction you are facing, aligning it with the front of the mob, similar to boats. As of 24w36a, this is no longer the case. This issue blocks MC-270552.

Steps to reproduce

1. Summon a camel or a tamed horse, donkey, mule, skeleton horse, or zombie horse
2. Ensure you are facing a different direction than the mob
3. Mount the mob

Expected behavior: When you mount the mob, you should face forward.
Observed behavior: Mounting the mob does not cause you to face forward.