As mentioned in the comments, trim/molding is probably the best solution for this. It will allow some movement and you could use the same species of wood and same stain as the stairs. This will be resistant to cracking, but will not create an equal surface.
In order to get an equal surface, I have had some success using paintable caulking. This won't work well if the drywall sticks out past the stairs. You would fill the gap with caulk and smooth flush to the stairs. When you paint just tape the stairs to get a straight line. Caulk is flexible so will resist cracking, but if you don't get it pushed far enough in the gap, it may shrink. BTW shrinking is worse with transparent caulk.
Agree, you should always avoid flush connections between differing materials.
You need the smallest flat D shaped trim which looks good to your eye. Pin it into the stair stringer only (not both sides of the gap as that can split the trim in time) and treat/finish it as if it is part of the stairs.
Oh and paint the wall before you fit the trim so you don't need to cut the paint into the trim.
If the stair and drywall isn't flush you need a thicker trim and you'll need to run it through a table saw to cut away the difference (over half the width of the trim) to make a shallow L shaped trim.