I don’t have any personal experience with self hosted webmail. I know there are a bunch out there and definitely both options that can sit in front of a maildir and options that can sit in front of a POP/IMAP server like Dovecot.

I did a little googling, and if I wanted to set this up, the first thing I’d check out is something like imapsync -> dovecot -> Roundcube.

Dovecot provides a really reliable maildir -> IMAP/POP conversion layer, and once you’ve got that, most things should work.