I can really recommend Mailcow, and if you have a Synology NAS, Synology Mail Server. Receiving emails is the easy part. Sending them is the tricky one. If you wish to self host at home, you will need an external provider anyway, like a cheap VPS for its dedicated IP. If you already rely on something external, you may just use an SMTP service, like AWS SES, what is dirt cheap on a home lab level. (I have not paid anything since I started to use them with my weekly 5 email sent.) I can also recommend forwardemail.net for catching emails for a domain or a specific email address and just forward them to any email address. For $3 a month, they offer an SMTP service, too, so you can use them to send emails from your domain.