Changes
HB was mostly right; until I can figure out how to only get the templates that transclude this template (and not any further down the pipeline) I'll just keep it at pages starting with "Template:Infobox". Also added a switch so that the (blank) cat text for this template isn't shown
{{#invoke:Infobox|infobox}}<includeonly>{{template other|{{#ifeq:{{PAGENAME}}|Infobox||[[Category:Infobox templates|{{#ifeq:{{str left|{{SUBPAGENAME}}|7}}|Infobox|{{remove first word|{{SUBPAGENAME}}}}|{{SUBPAGENAME}}}}]]}}|}}</includeonly><noinclude>
{{documentation}}
<!-- Categories go in the /doc subpage, and interwikis go in Wikidata. -->
</noinclude>