Allow each wiki community to add (via a wikipage in json format in the `MediaWiki` namespace) a list of templates that they think are particularly useful to users, and display those in one of the tabs in the template picker
The UI in the template picker could be something like this {F59546712}
(but without the "add" link, or the "favourites" list - image from Commons, see https://commons.wikimedia.org/wiki/File:Easy_access_Templates.png)
The CommunityConfiguration extension allows us ways to define/validate a config schema - we could use a wikipage for config even without it, but it's safer and easier with. We'd need to create a schema inside TemplateData, and set up the attributes correctly in TemplateData's `extension.json` (and I guess this would mean TemplateData would have a dependency on CommunityConfiguration).
Obvs we'd also need this to get buy-in from communities, and for them to actually add some templates to the relevant config page, before we'd deploy
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Note that there's already been similar work done, but as a patch to VE rather than TemplateData https://gerrit.wikimedia.org/r/c/mediawiki/extensions/VisualEditor/+/510943