You were actually very lucky to get the cutting that you did. But, taking the advice to out it into water was ill advised and now you have rot.
I answer a lot of these questions, because I have been growing these variegated monsteras since c2002 and have propagated many times. I try to present facts, so these are the facts. I realize it may be too late for this to be said, but, in case you ever do this again, it may help.
Monstera are epiphytic plants. When they grow in the wild, they do not start in potting mix, moss, or water. (When did you ever know a plant, other than a true aquatic, to root itself in water?) Monstera actually start out life up in the trees above the forest floor on a host of some kind. Usually a tree where a bird or small mammal has dropped a seed, which germinates on the leaf litter and other detritus. The plant forms roots that adhere to the host and travel down the host until they reach the forest floor, where they enter the soil and branch out. Until they reach the floor, (which can be over 30 feet of traveling down) the adventitious roots are totally capable of absorbing water and nutrients to sustain the plants.
That said, you did not need actually, with that very nice root that the person graciously left on your cutting (most sellers chop the roots and you have basically a worthless stick), to 'root' your cutting any further. It was already rooted. Planting the adventitious root would have caused it to start branching and creating soil roots on its own. All you needed to do was treat the cut end (the end closest to whatever that yellow thing is) with a fungicide and plant it in a small container of whatever substrate you chose to use.
Now though you have to deal with the rot, which unfortunately seems to be extending now to your root.
You need to take a sharp blade, like a craft knife, and start very carefully debriding the rot from the stem, cutting to clean tissue. This may cause you to have to sacrifice your root. I hope not, because that is your only, lonely node. You also have a very nice new shoot already formed. If your root gets sacrificed and the rot has gone through the nodal tissue, you may not have enough left to form a new root. Monstera produce roots from one side of the stem and leaves/shoots from the opposite. A new root will generally not form on the same side as the leaves/shoots and vice versa.
You can take the approach of excising carefully enough tissue to leave the root, and treat very well with fungicide and hope that it is enough to stop the advance of the rot and heal over, it may, or it may not. If any of the distal end of your root is mushy with rot, you should cut the root above the rot and treat that with fungicide too.
Putting it in moss would be the best thing, but if you have to wait days for it, it could arrive too late. Do you have any perlite that you could use? Or any fir bark? If you have some things that can help lighten the soil-less potting mix and make it more porous that would help. But, the most important thing is to address the rot and treat with fungicide. If you don;t stop the rot, it won;t matter what you pot it in.