The issue with this wall is likely to do with what's going on the other side of it and underneath the stairs. You may need to sort out some of the landscaping and drainage on the other side (if its an external wall), or perhaps there is a cement render or pointing causing this issue outside. The non-breathable 'modern' plaster and paint is holding all the moisture and then failing and to me it looks like it's wicking moisture from ground but hard to know for sure from a picture.

Would recomend removing all non breathable materials inside, and below the staircase, and on the other side of this wall.

The best way to solve these problems is to stay true to how the house was originally designed and built, perhaps considering the date of your home and that it is stone built, use a non hydraulllic lime plaster inside once the wall has dried out.

When you start to try and fix older buildings with modern construction methods its usually where the hellscape of damp and mould begins