Sorry, no, no no, no sand, unless it's very COARSE, it's the worst thing to add.

Perlite or Pumice, along w/ C&S, mixed 50/50 would have been an appropriate mix.

This plant, a Euphorbia, lactea I think is likelier thirstier than the Haworthia sharing its pot, I'd move the Haw out to a small pot of its own.

I defer to folks who grow this as I don't, but I'd guess you need to remove the rotting branch on the left & cut it back 'til you find healthy tissue.

As Karen said, I'd put it in a mix that has a lot of pumice or perlite in it, no sand. I use a mix of pumice, lava, a little turface, and chicken grit for my Euphorbias. I would remove that rotted part from the pot.

I don't really agree that the Euphorbia would be thirstier than the Haw. If anything, I water my Euphorbias less often than my Haws, although I don't have E. lactea, and my Haws are in pure pumice, lava so they drain and dry out pretty quickly. I do think that the Euphorbia would like more light than the Haw.