Blender 4.2.1
My paste flipped wasn't working
Trying to make it work, in Object Mode, I selected the armature, Ctrl + A and applied Rotation & Scale. Then, in Edit Mode, I selected all bones, ⇧ Shift + N (Recalculate Roll) and View Axis.
Doing that, I was now able to paste flipped, but my character's leg and IK foot controls broke.