Always glad to see the animator's survival kit as reference 😃
Regarding your question, You need to have different approaches on walks depending if they're frontal or lateral.
The limbs of a lateral walk can be mirrored by animating one leg and one arm, duplicating the keys on the other leg and arm bones, then offsetting said keys so that they'll play at the correct time: Dopesheet - Spine User Guide: Key Offset
A frontal walk follows the same steps of the lateral one, but requires the bones to be flipped to mirror correctly. The easiest way to do so is to scale at -1 a parent bone: Spine: Tips: 46 duplicate limb
If you copy the bone transforms in local axis you can also achieve the same result (to copy paste single frames/bones positions) Tools - Spine User Guide: Transform copy