I would join one side of the pedestrian area to the road way nodes as is done in the link above so that routers can route pedestrians across the area.
Edit: not a good idea in view of the Vincent de P... post
In this case the footway performs that role anyway. I have seen pedestrian areas before that are isolated or islands and unconnected to other ways so are unable to be utilised by routers.
Routing example of your pedestrian area:
https://www.openstreetmap.org/directions?engine=graphhopper_foot&route=36.06804%2C-79.81132%3B36.06751%2C-79.81032#map=19/36.06777/-79.81083
An equally viable alternative would be to outline the paved area of the pedestrian way as viewed on the satellite imagery and have short segments of footways linking usual foot traffic routes from the pedestrian way to the road, especially on larger pedestrian areas.