I think the most helpful aspect for search is a consistent translation. As long as “tag” is always translated with “Schlagwort,” you don’t need to add that as a keyword. (In cases where it is not, like site_settings.remove_muted_tags_from_latest, it’s better to improve the translation.) And in cases where a keyword is used in the English description, it’s probably also helpful to have it in the German one. So, in the case of the description of contact email:
English
Email address of key contact responsible for this site. Used for critical notifications, and also displayed on /about. Visible to anonymous users on public sites.
German
E-Mail-Adresse einer verantwortlichen Person für diese Website. Wird verwendet für kritische Benachrichtigungen und unter /about angezeigt. Sichtbar für anonyme Benutzer auf öffentlichen Websites.
The German translation could be improved so that “Kontakt” is included, and searching for it returns the setting. However, this won’t help for site contact group name and site contact username because the English description does not contain “contact”; it’s just part of the name. In this case, a translated setting name would help. It would be even more helpful if it was not just a keyword, but if both the setting name and its translation were visible in the interface. Because the additional context the setting name provides is not only helpful for search but also for understanding the description of the setting.