Todoist would work great for this. Projects can be shown as a list or a board (configurable), and you can have sections like “todo”, “doing”, and “done”. In a board format, these would be similar to a kanban board, except for the “done” automation — when you’re done, you need to tick the task card. You also get assignees, due dates, comments, attachments, native apps everywhere, and so on.

We’ll be able to tell with real comparative data now that both options are available, but I’d be shocked if SQLite itself is the bottleneck, especially in a low concurrency scenario (which is the case for most installations of star apps).