When a player is riding an entity that is teleported with relative coordinates, the ride entity does not interpolate smoothly. The previous resolution was only applied for minecarts when using experimental minecart enchancements, but it should work for ALL entities. Please look the attached video: 23w38a + Experimental Minecarts.mp4

Steps to reproduce:
1. In a repeating command block insert the following command:

execute as @e[type=minecraft:armor_stand] at @s run tp @e[type=minecart] ^ ^ ^-2 

2. In another repeating command block insert the following command

data modify entity @n[type=minecraft:armor_stand] Rotation set from entity @a[limit=1] Rotation 

3. Summon a minecart (or any other entity) and an armor_stand

4. Ride the teleported entity

/ride @s mount @e[type=minecart]

5. Look around while riding the entity

Observed result:
Your camera is shaky, and the ride entity detaches from the player

Expected result:
Your camera does not shake and the player follows the player, like in 1.21.1

Notes:
After multiple edits, we've figured out that the problem is caused by teleporting with relative coordinates and only seems to happen when the player is riding the entity, so its probably the same bug as MC-275767 but not completly fixed.