Why not postfix?
Look at ISPConfig.
It isn't simple but has all of the services you require:
postfix (SMTP)
dovecot (IMAP)
LMTP
MySQL databases for management
Web-based management interface
I like to use hmailserver just because it's very easy to set. But being discontinued i keep it inaccessible from outside the network.
If you set up MX records inside your intranet you can go for a really simple setup with postfix. https://www.postfix.org/VIRTUAL_README.html#local After that you should be able to use mutt on the command line via ssh on your postfix virtual server to read the email. If you want webmail though, things will take more time and reading howtos ;-)
Have you looked into self-hosting NextCloud or OwnCloud?
From what I understand nexcloud isn’t a mail server, only a client. I’d need something that can act as an SMTP bridge to actually send emails.
It provides a web interface for mail (and other useful services). You configure it to send outgoing messages through SMTP, qmail, Sendmail, Postfix, Dovecot, take your pick for the back-end.
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