Teleporting a mob while riding it will cause a visual glitch and deviate the rider. The following example uses a chicken as the vehicle.

Steps to reproduce

1. Run this command to summon a chicken: 

   /summon chicken ~ ~ ~ {NoAI:1b, Saddle:1b, CustomName:"\"chicken\""}

1. Set up a repeat command block with this command: 

   /execute as @e[name=chicken] at @s run tp @s ^ ^ ^0.35

1. Run this command to ride the chicken: 

   /ride @s mount @e[name=chicken]
   

Expected Results

The player rides the chicken without any offset while it goes forward, like in Minecraft 1.19.4. (video: "1.19.4_ride_expected").

Observed Results

The player rides the chicken with a offset and it shakes while it goes forward. (video: "23w18a_ride_bug").