By default, navigation for pedestrians will follow the roads (just like cars), and the only purpose of zebra crossing nodes is to alert motorists.

I added a few connectors here, all around the intersection.  Give 2-3 days for GraphHoppers engines and other to refresh their data and they will start routing around the footways if it's shorter.
https://www.openstreetmap.org/way/1327815334

You can draw more sidewalks from this structure if needed.