Basically what I said. Dovecot can be installed on every Linux or BSD system. You’ll need Pideonhole and FTS Flatcurve as extensions.
When you install fetchmail, you can let it connect to all your IMAP or POP3 servers. Each process will deliver your mail instantly to your own Dovecot server.
You’ll also need a certificate for Dovecot. This can be solved using Letsencrypt.
You can use any mail client you want. I use Fairemail on Android. On desktop and notebooks it’s Thunderbird.
With an IMAP server you have the power to serve your own emails. fetchmail will deliver them constantly to this place. You have all emails in one place and you login just to your own server.