I have the interface set to English and my language fallback chain includes German, but I see a number of items on Special:Nearby where the label is shown as "No label defined" when the item has a German label and/or no description is shown when the item has a German description.
|Open||None||T124286 [Epic] Wikidata language support|
|Open||None||T76216 [Epic] Language fallback|
|Open||None||T117158 Special:Nearby should use language fallback for labels and descriptions|
If I switch the interface language to Danish, it gets weirder. Some items only show the ID, some items show "No label defined" (in English...) and the ID in brackets and some items show the English label.
I checked all the items shown, none of the items have Danish labels, all have German labels and some have English labels. All the ones which show the English label have English labels (obviously) and all the ones which show "No label defined" don't have an English label. All the ones which show only the ID have English labels too. It appears to sometimes fallback to English, sometimes not, and never fallback to German.
"No label defined" comes from the display title, which doesn't always exist. When there is a display title, then it is not multilingual and is cached in one language (usually english, but not always)
I don't think we want to have display title in nearby for Wikidata and need to investigate it more ...