https://commons.wikimedia.org/wiki/File:BrunnenHaydnplatz.jpg is tagged with {{Object location}} and does not have a {{Location}} (at the time of writing).
The API call https://commons.wikimedia.org/w/api.php?action=query&format=jsonfm&prop=coordinates&titles=File:BrunnenHaydnplatz.jpg&coprimary=all does not return any coordinates at all.
T105593 seems related.
The Commons template Template:Object location passes mode "object" to Module:Coordinates, but the module only triggers GeoData if the mode is "camera".
Thanks. This explains the technical reason why {{Object location}} does not show up.
Has there been a discussion whether or whether not to consider {{Object location}} as "geographical coordinates" for the Extension:GeoData?
Depending on the photo, {{Object location}} is more suitable to describe the location. Also, when {{Coordinate}} is missing, {{Object location}} might be a sensible replacement. The Wiki Loves Monuments upload wizard favours {{Object location}} (see T72437).
Would that discussion belong on Commons rather than here, since it has to do with Commons policy rather than a technical matter?
I started a discussion on the {{Object location}} template here: https://commons.wikimedia.org/w/index.php?title=Template_talk:Location&diff=244766131&oldid=235858819