Currently, the translations are defined by the page WorkspaceManager.Translations and are located in the main wiki. Workspaces are aware of this and are explicitly using the page from the main wiki as translation so that the menu looks ok.
A regular subwiki does not know about this and does not use the translation document, thus showing only translation keys.
The workspace application needs to use ApplicationResources.properties to provide its translations so that they are visible on all the wikis.
Workaround for subwikis:
Go to the subwiki Administration>Configuration>Localization and add to Internationalization Document Bundles the page "xwiki:WorkspaceManager.Translations".