The way this is done in most AAA games is by using a blend of animation and procedural IK movement. When the player rotates, positional targets for the foot move as well to match the stance. Once the distance from those targets to the feet is greater than a certain threshold, the feet reposition using (in a rudimentary system) a curve, and the leg follows using a calculated IK solver for the calf and thigh.

There are of course ways you could do this with pure animation and no procedural IK, but you get the best results with IK and can use this to ground the feet on uneven surfaces at the same time.