For the page description (Wikidata description override) the last instance of the magic word {{SHORRTDESC}} is used. This is awkward as editors want to put the description on the top of the page (which is where you'd expect a summary to be), and they want to provide fallback values via various templates like infoboxes, and those templates come later, so the fallback takes precedence over the real value.
SHORTDESC should support {{SHORTDESC:...|noreplace}} like DISPLAYTITLE and other things do, so that templates can mark their values as fallback ones.