How can I save my succulent?

I recently repotted my succulent into a bigger pot as it had outgrown its old one. However, yesterday I saw it had bent over. I propped it back up, only to find it bent over again. For now I’m using a pencil to prop it up 😅

I’ve also noticed the bottom parts of it have started to get kind of mushy and wrinkle up, although the top seems fine. I’m not sure what this means, but it’s probably not a good sign. I also noticed that the top of the plant has kind of separated from the bottom (it’s still connected but not very well) so I don’t know if I should just detach it entirely and repot that??

I was also thinking maybe the soil I used isn’t right for it? Any soil recommendations would be great!

Sorry for the lack of better plant vocab… clearly I’m not really sure how to deal with this, so any help would be appreciated. I’ve had this little succulent for a while now and would be sad to see it go. 🥺