In my opinion, the second one is goner. However, you can save it in a way.

Get a sharp, clean knife and cut the top off above the bad area. The interior should look damp and clean with no sign of the deteriorated area of the plant. If you still see a bad spot, cut again until you see all clean tissue. Set it aside out of the sun for at least a week so the cut edge can dry up. or callus.

Get cactus and succulent mix from the nursery (you can get a better mix if you also get perlite or pumice to mix with it 50/50, but at the least get commercial cactus/succulent planting mix). When the bottom of the cactus is completely dry, plant it in the mix you got. Do not water until your cactus has started to grow roots, which could be weeks. Don't worry, it has a lot of moisture stored so it will survive. If you water, it will rot because it has no roots to take up water.

As for pots, you could use that little pot it was in if it has holes in the bottom and if you do not double pot it as it was. If you buy a pot, get a small clay pot. Your plant does not want to be in a large pot. It died because of being double potted and the soil isn't fast draining enough and was holding too much water.. Also, it was probably not getting enough sun. It needs full sun, but transition it gradually to that much light.

Others know more than I, but I would repot the euphorbia in a slightly larger clay pot. The little buckets are cute but are not helping your plants survive.