Background:

Extension:CreateRedirect is a nice little extension that helps manage redirects:

https://www.mediawiki.org/wiki/Extension:RedirectManager

It might be a candidate for bundling or integration into core, but lacks some functionality, which we'll deal with here:

Wikipedia uses a variety of {{redirect templates}} to categorise its redirects:

https://en.wikipedia.org/wiki/Category:Redirect_templates

Proposal

In Extension:RedirectManager, it should be possible to add and remove redirect templates (plural) to the redirect. Some pages might need more than one template on them, e.g. a plural redirect to a disambiguation page.

For that, you're going to need a curated list of all redirect templates, e.g. at [[MediaWiki:Redirect-template-definitions]], a drop-down and the ability to select more than one of them at once.

There is some overlap here with T393673: Extension:CreateRedirect: Add redirect templates.