When a player is riding an entity that is teleported with relative coordinates from another entity, the ride entity does not interpolate smoothly. This issue is more noticable with a minecart: video.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 and an armor_stand

4. Ride the minecart

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

5. Look around while riding the minecart

Observed result:
Your camera is shaky

Expected result:
Your camera does not shake, 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.