Deleting a featured template results in the action=query&meta=communityconfiguration API returning an error and so the feature templates tab displays nothing at all.

Also, it becomes impossible to edit featured templates via the CommunityConfiguration form at Special:CommunityConfiguration/TemplateData-FeaturedTemplates; it returns the following error:

Failed to load a valid configuration from the Featured templates (code TemplateData-FeaturedTemplates) provider, see MediaWiki:FeaturedTemplates.json.

The only workaround is to edit the JSON directly to remove the deleted template.