Hi, 

I've split the stairs in to two stairways and footpaths respectively (positioning based on satellite images), added the step_counts you mentioned to the respective segments, and added handrail=yes to the first section of stairs (with three steps) based on your picture. 

I was unable to see in it if the second stairs also had handrails, so left that set to no as it originally was.

Changeset is here:
https://www.openstreetmap.org/changeset/152000416