From the awesome logged-out contributor at https://www.mediawiki.org/wiki/Topic:Tqefilkhr1iqupw2:

Issue

It is currently impossible for a user to differentiate templates (either programmatically or with tools) without using categories.

Use cases

• Discourage certain templates in certain namespaces - e.g. Template:documentation (documentation type) in main namespace
• Create specific tools to target specific templates - e.g. a customized infobox editor, visualeditor / wikitext editor insert dialog for specific types of templates
• Retrieve data related to specific templates - infobox templates provide rich data that can be used in many contexts (search, translation, mobile apps, etc), but it is impossible to differentiate an infobox template from a "quote" template.

Proposed solution

Add a new property:

<templatedata> {
template-type : "infobox"
}</templatedata>

Categories don't really work for this because many templates are over categorized or mis-categorized.

There is a similar extension by wikia (https://github.com/Wikia/app/tree/dev/extensions/wikia/TemplateClassification) that might be worth forking. It seems to use some heuristics to automatically detect the template types, and also allows editors to overwrite those (see wikia's Help:Template types).