I recommend (a recent) ejabberd if you don't know anything about XMPP: it does an excellent job coming with good default, clear, commented and foolproof config

I recommend (a recent) ejabberd if you don't know anything about XMPP: it does an excellent job coming with good default, clear, commented and foolproof config and once it's running you can literally forget about it. XMPP does manage offline message catch-up across all devices, and with good mobile clients I've never felt the need to redirect to email (especially these days with ubiquitous E2EE, that's not something you would want the server to be capable of doing), that said I believe it would be "easily" scripted up.