Earlier quoted context omitted.
I made a very extensive search for an open-source webmail solution that exported a REST api. Unfortunately, none of them do (that I could find). Most of them are from the XMLRPC days. I'd definitely contribute to a kickstarter for a good FOSS REST Email server.
| good FOSS REST Email server You should specify what you're talking about here. An all-in-one solution? An SMTP server? An IMAP server? A webmail client (e.g. SquirrelMail / RoundCube)?
Central app that manages the storage, sending (server to server) and receiving (server to server) of email exposed over a rest api