The body of the cactus is in great shape, but it seems like whoever tossed it ripped out a lot of the root ball. There are still roots, I just worry about the roots dying before it can reestablish itself

6

Get a dry ass cactus soil mix, or go to a local greenhouse and see what they can give you. Get some rooting hormone powder, sprinkle some onto whatever is left of those roots and stick it about an inch deep into a 6 or 8 inch pot with good drainage. DON’T use a clay pot, those will retain moisture, I recommend the standard plastic ones. Give it a light amount of water just to promote growth but not to much bc it might be stressed from going without soil. After it’s stable feel free to water

6

honestly just put her in an appropriate sized pot and let time do its thing. water when soils dry throughout the pot or if the cactus feels soft or extra wrinkly

5

is that not a euphorb? (sorry i know i'm insufferable)

2