I'm not sure why this is happening on this file as I've done it before. I am using empties as parents to move my character about the scene and when I export they don't retain their animation info. I also managed to fix an issue I had where the mesh origin on the imported FBX kept going back to the world origin and therefore would distort as it was still attached to the bones.
I am exporting to another app Omniverse (I'm aware Omniverse takes USD, I'm just testing in FBX) and am just showing the FBX in Blender for demonstrative purposes.
File export settings for both FBX and USD as well as their outcomes beside them:
Part of my anim, he grabs the crate and walks away.



