Players' capes detach from their bodies when moving

The Bug:

Players' capes detach from their bodies when moving.

This issue was not present in 1.21.1 and was first introduced in 24w33a.

Steps to Reproduce:

1. Ensure that you have a cape enabled.
2. Begin sprint flying, enter third person, look directly downard, and look at how the cape is positioned.

Observed Behavior:

Players' capes detach from their bodies when moving.

Expected Behavior:

Players' capes would not detach from their bodies when moving.