Moisture control, older house on a hill

We bought a small older home that’s situated on a hill. It’s a relatively dry climate in NE Washington. The bedroom was a later addition on a slab and seems to have some moisture coming up through the foundation, as humidity in the room is considerably higher than the rest of the house. The east wall of the bedroom and the house faces the hill, with about an 8 foot tall sloping rock wall and then more slope above it. The slope and rock wall continue around the north side of the house but decrease. There is a french drain on that side, but I suspect that much of the moisture is coming from the east side where there is no drain. There is about a 30″ space between the wall and the base of the sloped rock retaining wall there, which some prior owner paved with concrete.
So, wondering whether it would be worth the trouble to saw up that concrete (about 4″ thick) and put in some kind of drainage system there. Looking for any and all suggestions for tackling it, or whether it’s not worth the bother, and if there are things to consider if we go forward with the job (like the risk of soil and the rock wall slumping) if we dig a ditch there. See photo for the most problematic area (east side)