I just noticed that the TemplateData included in https://de.wikipedia.org/wiki/Vorlage:Internetquelle/Doku?veaction=editsource via template is not recognized by the "Manage TemplateData" dialog. Using this dialog will not edit the existing data, but add a second (redundant) TemplateData block to the page - as can be seen in the page history:
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This seems like a excellent reason to get your community to not include templatedata via a template. Pretty much every other wiki doesn't do this.