They use a single coin cell. Last a good long while, like several nights.
The horizontal ones can be found on Amazon and are rechargeable. They are prone to falling off so I removed the internal spring and glued them to my shoes.
Thank you so much :) the converse pair took me forever. I embedded electroluminescent wire around the sole. The other two (the vertical lights) were easier to make. I've made a green variant that is like stacked power bars that you can see at https://www.jilanico.com
Love that you call them 'mag boot style' and reference the Expanse. Those novels were great and the TV show killed it with the visual style. I think you captured that really nicely. Excellent!! Your IG is on that link?