Hey @jmxt! Here's an example app based on Everett's solution
To @bfelbo's original point of having a Postgres-backed kanban and Everett's suggestion of using a List View, you can also filter the data returned from your database by category and then reference each of the resulting datasets in a separate List View. Nested List Views even let you set the number of categories dynamically!
There are a number of different ways to structure this, and it does take some extra design so I definitely suggest going with what's most comfortable for you.