That soil looks water retaining. You should improve drainage by adding lots of sifted perlite, or pumice if available. Adding about half will help a lot - small handfull is not enough. Unfortunately, C&S sol is often not as well draining as it should be. You can't go wong by adding as above to a mix used for potting any succulent.

The 'moon cactus' is just a marketing name. It is actually 2 different plants - bottom is a vigorous rootstock and top (red in your case) is a plant that can't survive on it's own because it doesn't have any chrolophyl. Top cacti often do not last very long time (sometimes they survive) even if grafted. I can't tell for sure what kind of problem it has, but it could be rotting. Try to feel if it is soft - if it is, it could be already rotted. Dray splotches may or may not be much of a problem, many cacti start corking with age. But I can't tell looking at your photo.

When repotting new succulents, do not use much bigger pot - often, same size is enough, or maybe just next one up. Mix needs to be much better draining, and there should be more of it in the pot so plant is not sitting too low inside. Succulents need lots of good light, many need lots of sunlight (they should be acclimatized to it), and good air circulation.

The top is still hard, so it seems it's not rotted. I will try repotting it with 50% perlite or pumice.

What happens when the top plant dies? Does it turn brown and fall off, and the rootstock keeps growing?

Better photo - clear close-up of the top - would probably help.

If rop dies, it may just dry up, Or it coud be mushy - rotted. If the rootstock is not rotting, it usually continues growing.

Just like Rina stated, the top cactus has no chlorophyll. Only the lower half can photosynthesize for both. So if it's not getting sufficient sunlight, then it can't produce enough food to feed both halves and the top half will be the part that suffers from it.

Whenever I see these, I can't help but wonder why they don't graft these cacti onto much larger root stocks. Probably because there's more profit in people just buying a new one, rather than maintaining one that's dying.

Hylocereus, the usual rootstock, is a fast and easy grower which can be produced cheaply. If they would use for example Harrisia jusbertii, the cost of producing the rootstock would make the plants much more expensive.