Published as https://codein.withgoogle.com/dashboard/tasks/4813731028533248/

By the way changes should be made to https://commons.wikimedia.org/wiki/Template:City/sandbox so they can be verified before going live.

Is this a one-time wikitext task to update the template, lua task, or a bot task?

This task is a recurring wikitext task, unrelated to lua or bots. The easiest way to deal with it is to:

1. clean up Category:Multilingual tags: Locations and make sure all the city templates are in https://commons.wikimedia.org/wiki/Category:Multilingual_tags:_Locations_by_country
2. Than go country by country through the [[template:city]] and compare cities with templates in sub-categories of [[Category:Multilingual_tags:_Locations_by_country]]. This task is sometimes done more easily with help of a spreadsheet where you can order lists.
3. alternative approach would be to capture all the templates in sub-categories of [[Category:Multilingual_tags:_Locations_by_country]] and than parse [[template:city]] and extract all the template names used there. Than compare both lists and capture city templates which are not in [[template:city]]. AWB's List comparer (https://en.wikipedia.org/wiki/Wikipedia:AutoWikiBrowser/User_manual#Tools) or a spreadsheet could be used for comparison.

By the way 2.8M pages use this template.

See also [[T89601]] for the Wikidata based approach.

Multichill, thanks for this link. I assume that that is how most templates in [[Category:Multilingual_tags:_Locations]] will be written in the future. [[Template:City]] is more of a Rolodex of existing templates, so alternative spellings of different city names are matched to a correct single i18n location template. Than that template can be written in the way you proposed in [[T89601]] instead of the crazy stuff we do now.