There's also mailcow that's popular in the self hosting crowd. Anyone use it and can share experience ? I'm a bit lazy to switch email since the other end of the mail is going to be gmail/outlook etc. anyway. So not much net gain.
I'm only slightly worried if they ever abandon the project I'm out of luck maintaining it by myself. But since it's all based on standard software it's rather easy so switch to another solution I guess.
So far, there seems to be no standard extension to IMAP to integrate with those, so you need some app which has a server side component to do it. (Which is exactly what Gmail, Outlook, Whatsapp, Facebook Messenger, etc. all do).
Edit: I don't remember if I had to whitelist k-9 under battery optimisations. Maybe that's a requirement to use notifications without gcm, as it's a common theme in all apps that support notifications without gcm. On Apple devices, you will be generally out of luck, but that's a foregone conclusion.