I am interested in webmail clients not because I want to run a multi-user server, but because desktop email clients for linux are not great and I am interested in running a single-user email client for myself.
Weird open-source alternative email client mailpile tries to be hackable and secure. AGPL-licensed, which is a mildly irritating licence. Reinventing lots of wheels and full of odd obsolescent dependencies. I like their aspirations, but their github tracker feels amateurish. Watch how they cargo-cult in an unmaintained Bayesian spam filter as essential infrastructure without the ability to maintain it! Thrill to their unclear threat model! Panic as they take years to get prototypes working! Or don’t. I won’t.
SOGo, “A Free open-source enterprise-grade Webmail and Groupware Server for teams”. Amazingly, written in Objective C. Not bad in practice, although a little over-engineered for personal use. Includes calendar and contacts in the groupware style.
pusto.org: Mailur is a lightweight webmail inspired by Gmail Source at naspeh/mailur. Python, actively developed, no database required.
msp301/pinbox: Self-hosted webmail client greatly inspired by Google Inbox (Go, suspiciously quiet)