Pulling back that carpet and popping off a piece of trim may revel some more clues beneath the shimmed sheetrock and towards the sill plate? If not, it will give you a chance to get things drying more quickly with a couple fans.
Correct me if I’m wrong but isn’t that the basement we r looking at? If the foundation is leaking that means the ground is so saturated it’s coming up and out?
Exterior wall will have plastic to protect sheetrock, water can travel on the inside down and out to what you are seeing.
I agree with Bucky. Pop off the trim, cut out the rock below the trim line and see where the water is coming. If your insulation is wet a good thermal camera might be able to pick it up still up the wall. Wet insulation is not good insulation
Since we are all throwing out guesses I’m gonna go with first deck board is sloped towards house having water leak down into whatever that exhaust housing is and leaking down.