When hiking the Appalachian Trail, many new hikers will fret over having to climb steep mountains and in preparation for a hike they will do a lot of cardio to prepare themselves. However, what they failed to realize is that it's the downhills, (despite being easier on the cardio system), that cause the real pain, i.e. injuries. This is because going downhill is much like doing a single-leg squat over and over and over... Many times resulting in injuries to connective tissues.
The take away is that as we age it's the musculoskeletal system that should be given more and more attention.
And that will help your stair climbing as well as your

There you go, everything applies to cycling