The path containing https://www.openstreetmap.org/way/1242210605/ is mapped as a footway. There are four flights of stairs mapped along its length. The number of steps is not specified, so it is probably difficult for a router to guess whether a real person would prefer to climb up or down the steps or to take the longer cycleway. Entering the number of steps might help if you're able to count them.

There's also no specific permission for bicycles on either the footways or the steps. If there's no signage prohibiting bicycles or requiring dismount,, adding bicycle=yes might encourage routers to suggest that route.