"Side-step" options for puppet procedural animation

When moving left or right while facing forward, the puppet's hips turn to face the direction being moved in, which doesn't always look natural. Especially if the upper body is "facing camera direction," it can feel like the lower half is completely disconnected and the character is snapping themselves in two.

Some games animate this direction as something of a "side-step," where instead of the lower half acting as though it's walking normally in the left direction, the hips stay more forward (which looks more natural) and the feet move side to side as they walk, or cross over each other a little bit. Kind of like this? https://youtu.be/_jYLMS2n8Hg

Maybe some other related settings would be required to help us dial in how it looks for our character and situation, but I think this could really help 3rd person games look even better!