I currently use the letsencrypt-auto client. There is now a Debian package for certbot to which I would like to migrate. Can I just install certbot and use it - will it pick up the existing letsencrypt data seamlessly or will I have to migrate it in some way?
Yes, the configuration should continue to work with the certbot package. The configuration directory is still /etc/letsencrypt, and the files are compatible as long as you’re not switching from a very old release of letsencrypt (which is unlikely with letsencrypt-auto, since it auto-updates).
I’d make a backup of /etc/letsencrypt prior to upgrading, just in case.