Around here, Many of the complexes for seniors have a certain amount of apartments for physically disabled (primarily wheelchair users)
Even when they advertise that they are taking applications (would make it seem like they have openings or expect openings) they typically do not have immediate or near-future openings. Typical wait lists are 6 months to 5 years... and some of the locations (safer areas of town, nicer or newer buildings) often have decade long wait lists (and, they still open for application from time to time, even with such long wait lists)
There are few different types of listings that I have seen:
1) Seniors 55+
2) Seniors 65+
3) Seniors 65+ or Mobility Assisted Disabled
Unless you also meet the age requirement, you would have to look for the ones that take applications for Mobility Assisted Disabled
Typical rent is 30% of your SSI/SSDI or 30% of total income (some folks who live there work) plus your utilities. Sometimes the apartments includes water & sometimes it doesn't
Even though I am mobility challenged to the point of needing disabled parking and needing a Service Dog to provide Balance/Mobility support, those apartments do not consider me mobility challenged enough... they need doctor verification of wheelchair used
In your case, that should not be a problem.
and, I understand the difficulty, I can't do stairs at all... and no apartment is required to provide me with a stair-free access to an apartment (walk-on level units often are rented off wait lists). So, it was difficult to find a suitable place to live. It took a while, but I was able to get what I needed.