If you shift your perspective, you may feel a bit better about stepping back.
Your kind attention has helped your friend remain in her home for as long as was feasible. However both of you are reaching the point where she needs to be in residential care, regardless of what she actually wants. The perspective shift is that the longer you maintain responsibility for her care, the longer you’re keeping her from the residential care where she can have 24x7 attention.
So yes, agree with other posters. Tell SS point blank that you are withdrawing all of your help and support, and that they must now assume this responsibility. Don’t enter into any discussion and don’t allow them to drag you into things like deciding which home should be used. You need to be mentally prepared to not answer phone calls, not respond to messages and not reply to letters.