The account management settings page mentions needing an application password for Gmail — you'll also need one to add a Fastmail account (it looks like it retrieves through IMAP and sends through SMTP).
When I added an account, the account's existing folders weren't displayed to me anywhere (I was expecting the sidebar), but it looks like you can add a column for an existing folder and it'll just work.
It also looks like the action of dragging a message from one column to another removes it from one folder and adds it to another, which makes sense for a kanban board, but might get a little weird with Fastmail's labels mode, where a message can exist in multiple folders! (https://beta.fastmail.com/help/receive/labels-beta.html)