Dimensions on your photo would help make a better model, but here is what I might do in this situation.

The easy way

End the upper trim with a bevel (30-45°) at the edge of the stair, then continue in the lower room as normal.

Transition

You may want to use a transition piece to pull the pieces together.

You could even cut an angle into the top of the transition, for a different look.

You may also want to bevel the upper trim into the transition piece.

The complex, lots of angle calculation, pain in the neck way

Cut a small angled transition piece from the upper trim, down to the lower trim.

In this case, you may still want to bevel the upper trim piece.

There's not really a right way to do something like this. It's more about your preference, and the amount of work you're willing to do.

It sounds like the dampness is still a problem in that particular area because it is a corner adjoining the external wall and the store area. Is this part of the house in shadow for a lot of the day?

1. Check the external ground area surrounding the outside store. If the ground is clay or compacted it might not be helping in that it is storing water. Perhaps better drainage there.

2. Some form of heating in the store area to keep it at a similar temperature to the kitchen e.g. condensation happens in that part of the kitchen because of the cold store area on the other side of that particular wall.

3. Perhaps a better seal on the door and windows in the store to keep it warmer in general.

4. Put a faux wall in the back of the store to buffer the cold air away from the wall that is adjoining the kitchen.

5. A robust kitchen extractor to remove as much steam as possible from cooking.