This "path" is a staircase.

via StreetComplete 57.3

There is a free standing artificial boulder located here for people to climb and train on. One of several around the city, I'll add the rest.

A few public exercise machines here

These traffic lights on a cycleway, unconnected to roads, look strange

This is just a path between these two stares

via StreetComplete 60.1

Attached photo(s):
https://streetcomplete.app/p/259428.jpg

Connection to the north path here

via StreetComplete_ee 60.0

Foot only connection

via StreetComplete_ee 60.0

Is this Spar now Asda Express?
https://storelocator.asda.com/yorkshire-&-humber/sheffield/craven-street

Unable to answer "Is this still here?" – Moor Bargains (Discount Store) – osm.org/way/1011032553 via StreetComplete 60.3:

Part of next? No gap between next and Greggs