Waterproofing a concrete basement wall with a staircase in the way?
I regards to the unsealed area behind the stairs leaking, you just have to get in there and seal up the unpainted concrete, and also patch any holes, voids, and the gap where the floor meets the wall.  We have done quite a few of these by removing a stair tread and in your case the riser so you can get in there.

For materials we always use Hydro-Seal 75 water based epoxy coating and apply two coats and do all our patching with Hydro-Seal 75 epoxy mortar which is Hydro-Seal 75 mixed with Portland Cement &amp; Sand(or concrete sand mix).  Hydro-Seal 75 is great for all types of basemant walls and floors


Remove stair tread and riser enough to fit a person in behind the stairs.
Prepare surface by washing with TSP &amp; wire brush after washing if needed.
Mix Hydro-Seal 75 enough needed to coat the area, looks like 1/2 gallon would do this area, and hand to guy behind the stairs.
Paint on with roller and cut edges with brush
Mixer makes some Hydro-Seal 75 mortar and hands to guy behind the stairs with putty knife so he can skim all cracks.  Allow paint and patching to dry 2 to 4 hours.
Apply 2nd coat same way to achieve a pinhole free application. I would also seal the entire floor behind there as well after 2 coats on the wall is done.
Put stair treads and risers removed back.


Note- Good job for a small person!