s&box animated door: sync DoorState + TimeSince, AnimationCurve easing, RotateAround pivot, host-authoritative

Developers building interactive doors in s&box often animate on the client only (causing desync) or use Lerp-based rotation that doesn't support custom easing. The correct pattern syncs state and time, uses AnimationCurve for easing, and routes all state changes through the host.