Forgot to mention that, sorry. They also work in StarterPack.
The problem seems to be that the animation will always be called a new instance every time the event is triggered. Since local RestingAnim = Humanoid:LoadAnimation(RestingAnimation)
Is called only in the prox-prompt, it keeps thinking you are trying to play and stop a new animation instead of referring to the same animation.
Potential Solution:
Use a BindableEvent or Remote Event to a server or local script that is in the player that can play the anim. That local script would be able to play the anim if you keep the anim being defined out of the OnClientEvent function.
You would then be able to replace the code in the prox-prompt script for calling the anim to just a remoteEvent to fire to the Player client (FireClient(Player)). In the local script, it will have the onClientEvent do the anim playing.