How do I move my Spanbox setup to a new computer?

Install Spanbox on the new machine from spanbox.co and sign into your apps there. Because it's local-first, your setup isn't stored in a cloud to sync automatically, you re-add your apps and log in once on the new computer. Your chats and mail all reappear because they live on the services themselves, not inside Spanbox, so it's really just signing in again.