Cinematic Camera motion remains after switching worlds / servers

The bug

The Cinematic Camera keeps its motion when switching worlds or servers. Expected would be that its motion is reset.

Reproduction steps

1. Assign a key to "Toggle Cinematic Camera" near the bottom of the "Controls..." settings
2. Open a world, activate the Cinematic Camera and start spinning
3. Close the world and open a different one
   The camera still has the remaining motion from the previous world

See (20w51a) Cinematic Camera keeping motion.mp4