We currently update the filter_counts table (which caches tag uses) in real time when users create new works or edit their tags. These are slow requests, and the counts don't really need up-to-the-minute accuracy, so we should handle this asynchronously instead, ideally adding the tag ids to a set and running a scheduled task hourly or every n hours.
Pick a medium and go to its page.
Pick a canonical fandom in that medium.
Write down the current count associated with that fandom.
Create a new work in that fandom.
Wait 1 hour.
Check the medium's page again and verify that the count has increased by 1.
You can also do similar tests with other actions that should change the count: e.g. deleting a work, adding or removing a canonical tag from an existing work, wrangling a tag, etc.