I had someone take care of my plants for 2 months and I came home to most of them struggling or dead. So sad!

A few large cactus limbs had fallen off and shriveled up EXCEPT there are baby cacti growing from the tops—my curiosity is, do I:
1. plant the whole large leaf into soil and see if roots form at the base of the original leaf
2. cut the larger cactus leaf in half/let it callous over/then put it in soil which might disrupt the new growth??
3. lay the larger leaf parallel to the soil so that the baby cactus can make its own roots into the soil like propagating succulent leaves

I'm including pictures. I've opted for a version of #3 for now but curious if it's the right move!

Welcome to the Forum!
I've had success with both options 1 and 3 for prickly pear. When the pads are flat on the soil, (as you have them in the second picture) they can form roots all along the underside.
If you plant the pad, just put about a third to a half down in the soil with the rest sticking straight up. When you see new growth, it's OK to water--a little. Use very fast draining, gritty soil in a fast draining pot.
It looks like you already have some new sprouts, that's a good sign that the plant is trying to grow. You could try potting up the one with no new growth just to see how option 1 works.
It's not quite like propagating succulent leaves, but similar. The cactus pad will form roots and support the new growth, not wither away as it grows.

Thank you MsDoe that is so helpful! Will follow your recommendation, fingers crossed.