I did this exact thing. the only difference between mine and yours is that i didn't have a brick wall to the side of my stairs.
Because my stairs were narrow like yours and I didn't feel skilled enough to notch the newell to slot over the string (and also because i didn't need a handrail for the stairs to fit into it) i did the following.
Cut a section of floor (highlighted green) out to expose the joist running parallel to my stairs (indicated by red)
I purchased a long newell base as I wanted the simple square design rather than any turned wood and cut it to height, i then cut a notch out so it could be fitted hard against the top of the string and the joist.
I coach bolted the section under the floor to the joist (not shown), and stuck a couple of L shaped brackets as well for good measure.
I then used two woodscrews (countersunk and filled) through the string into the newell (indicated by blue).
the post is nice and solid and looks the part.
i also bought a half thickness post for the other end which I just screwed into the studwork i put in to create the partially built cupboard you see in my pic.
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