Your problem is that POT. I'll bet there are no drainage holes at all. Am I right? Your cactus has rotting roots, less ability to take up water and so it is not able to store enough water in the above ground plant...thus the wrinkling.
You have to transplant this plant and any other plant you've planted in a pot without holes into slightly larger pots WITH holes using only potting soil. No gravel or rocks beneath the soil and above the drain hole. Lift bottom of pot off surface of saucer or counter using 'pot feet' or pieces of 1/4" tile. Breaks the surface tension and capillary action of water.
You've got stagnant, stinky water and anaerobic decomposition happening in the soil below your cactus. Not healthy for any kind of plant. Even aquatics!
Dump that out, allow whatever soil falls off to be disposed, transplant into a shallow (versus tall) pot, clay is best (breathes)...6"diameter by 3"high" Potting soil. Don't water until soil is dry. Don't need to soak the entire pot of soil. Keep it in what ever space it is used to. Let me know if the water and soil in that pot aren't horribly stinky.
Or if there is a hole in this metal pot. Or if you had rock/gravel beneath the soil. I am only able to assume by your pictures and words. Cactus have shallow roots for shallow rain spells in the desert. Soaked soil with no outlet no air exchange... causes rot. Not only for cactus and succulents but all plants including aquatic plants.