Self-hosting email fully is tedious/unnecessary, but what you can do is mirror your various inboxes (Gmail, iCloud, proton, non-corporate outlook) with mbsync and use roundcube or some other frontend to view emails and compose.
I use this to easily access mail from different services, and I can also send from any of them.
I also have a seperate service that watches the mail directory and sends a ntfy.sh notification for new emails.
It’s a bit complicated cause theres so many services but here are the quadlets: https://github.com/ebrahim37/infra-template/tree/main/homela...
I implemented this about a month ago because the iphone Mail app was increasingly buggy.