`Player#setPlayerProfile` causing desync issues

Expected behavior

Player#setPlayerProfile to set the player's profile and update the client, while keeping everything else properly synced.

Observed/Actual behavior

Player#setPlayerProfile seems to cause desync issues, for example:
If a player's profile is updated while riding an entity, it'll appear as if they dismounted to them and they'll be able to freely walk around, but once they actually dismount they'll teleport back.
This happens for other things as well, such as leads.

Steps/models to reproduce

1. Add a plugin that runs player.setPlayerProfile(player.getPlayerProfile()) to a 1.19.3 Paper server (see the test plugin linked below).
2. Mount a horse.
3. Trigger that plugin.

Plugin and Datapack List

> plugins
[23:06:30 INFO]: Plugins (1): test

> datapack list
[23:06:55 INFO]: There are 2 data packs enabled: [vanilla (built-in)], [file/bukkit (world)]
[23:06:55 INFO]: There are no more data packs available

No plugins or datapacks other then my test plugin.

Paper version

> version
[23:08:55 INFO]: Checking version, please wait...
[23:08:55 INFO]: This server is running Paper version git-Paper-362 (MC: 1.19.3) (Implementing API version 1.19.3-R0.1-SNAPSHOT) (Git: 52718db)
You are running the latest version
Previous version: git-Paper-360 (MC: 1.19.3)

Other

The plugin I used for testing: https://pastebin.com/1hdqmLw0
A video of the issue:

https://user-images.githubusercontent.com/31237389/209587838-015a8a8f-0262-43f1-9f8a-79c8d3537cf5.mp4