Stringers are the zigzag style angled beams that hold up conventional stairs.
![stringer](https://i.stack.imgur.com/nYamt.jpg)
They are used on each side ot the staircase and sometimes in the middle as well. They hold up the treads and the risers (the vertical boards) are attached to them.
Image 1 is basically floating treads on the stringers and using the risers as faces of drawer fronts. As the comments reflect, this is easily done when building a staircase, but quite difficult to retrofit. It also won't work if your treads are wider and there is a stringer (or the need for a stringer) in the middle.
Image 2 is a hybrid. There are no stringers on the near face of the staircase in the area of the drawers, and none in the middle. There may be conventional stringers above that level. It appears that there are horizontal and lateral supports built around the drawers and supporting the treads in place of stringers. Again, something that can be done when building a staircase, but not practical as a retrofit.
Image 3, based on a comment by John Smith, leaves the staircase intact, preserves the supporting stringers and gives you flexible storage possibilities.
The weight of materials in the drawers is not really a consideration unless you plan to store gold bars or some other really heavy materials. The weight of people on the stairs is much greater than any strain from linens or even books.
Best Answer
Yes, a landing is required at the top and bottom of residential stairs. The simple answer is it should be 36" in the direction of travel. (There is an "exception" to that, but does not apply to you. )
To solve your problem, (and I get points taken off my "reputation" for offering advice that doesn't stick to the question, but I'll offer it anyway...) try a 2 or 3 step winding step stair (pie-shaped treads) for the last few steps. Basically you're making a 90 degree "left-turn" at the top of the stairs. There are several requirements to those steps, which I'm not smart enough to figure out, but basically each step should not be less than 6" wide "where you walk". Where-you-walk is defined as a point 12" from the narrowest point of each step... Oh, the widest depth of a "winder " step can't be more than 12" at furthest point out...
Don't forget the handrail (mount between 32" and 38" from nosing of each step.) Handrails in residential construction is required on one side of stair only.