additionally, the aloe vera have brown spots on their skin, which I originally thought was sunburn or something, but could be browning from rot

In my experience with root rot, the roots are rotting due to too much water, poor drainage, wet plus cold... In these cases the roots are actually rotting and are mush. What you’ve described sounds like they were in need of a drink to me and it sounds like you’ve provided that.

In repotting it’s the same typical advice that you’ve probably seen if you’ve been reading posts on this forum. Growing medium should be well draining. At least half perlite or pumice with the other half being a commercially prepared cactus & succulent mix. That’s a good basic mix that a lot of people use. And of course your pot must have a drainage hole. Not following those two basic things is inviting root rot for sure.

If the roots were dry and brittle due to lack of water, they may need time to adjust to their new growing conditions. If they were mine, I wouldn’t water them any more for awhile. At least a couple of weeks.

Good luck with them. I don’t know what ruby cactus you mean but aloes are pretty hardy and forgiving provided they have good drainage and proper light.

Tyler gave excellent advice above.

If roots were dry and brittle, they my hve been dead (dried out). Dead roots will not come alive by watering them. It is suggested to trim off all dead, dried or rotted or otherwise damaged roots before repotting.

In general, succulents store lots of water in their sems and leaves, and will survive if not watered for a while.

It is always better to post photos if asking questions.