Puppet's legs are squishing in weird ways when in walk cycle

I would try adding sticks in the foot, which should help retain some of the shape. Also experiment with moving the heel tag higher. I think the gap between the heel and ankle is probably responsible for this. Usually we see flat feet so having them slanted up in heels like this is an interesting difference but it should work in some way.

I don't know what is wrong, but the knee (and maybe hip) positions seem a bit high to me. But no guarantee it will fix it. One trick is to turn the yellow mesh on (bottom left corner icon) and see how it is warping - sometimes it spots areas that look strange that are worth investigating (e.g. a stray handle or something).

I was also not sure about profiles - normally you have a "Left Profile" and "Right Profile" above the artwork so it knows the right walking direction for left/right. Maybe you added those tags to an existing layer?