[MCM-1144] Player movement when riding things is not in sync with itself

Partner Rank: 2

Verification builds: 1.16.100.50, 1.16.100.53
Regression builds: 1.16.20.3

Summary: Player movement when riding things is completely busted, including in vanilla

Impact: Player movement is something we all rely on in every aspect of the game. If the player doesn't control as expected it negativly impacts not only the marketplace but the entire game experience. Many maps use riding and many things can break when the player isnt in the position they should be. Papercraft 2 is completely unplayable for one of the quests.

Repro Steps:

Start the repro world Arrow game
Get in the minecart
press the button
just TRY to hit some of the targets that are ridiculously close to the track

Expected Results: Arrows should shoot from the position of the player, even when riding things.
https://www.youtube.com/watch?v=GesCwtsD59M&feature=youtu.be

Observed Results: Arrows shoot from where the player was many, MANY ticks ago even when playing locally. I might expect to see that sort of behavior on a server when im lagging out, but not locally.
https://youtu.be/19U_VyVThdQ

vanilla: https://www.youtube.com/watch?v=krJXKTdBYSY

Screenshots/Videos attached: above