hm, sounds like literally any regular webhosting service that also offers email (like every such service i know of) to me, then maybe used together with imap (or pop, if you wish), and if you want to connect servers with it to send mails, then “smarthost” or “sattelite system” should be the configuration you are looking for for your own MTA. to get received emails from that service most common is to use pop3 (still common because seemingly every service offers it for compatibility) but other protocols would be faster like immediate recieve using notify within imap, and there are other options too, but those depends on what that service offers like maybe sending your mails once received by them to your own server via smtp or by other protocols depending on what they implemented. i think there is no “twist” with that and -what i understand of what you want - is a quite common thing.

i for myself don’t want 3rd parties to be able to directly read my emails so i run my own mail server as tiny rented VMs from providers while my real emailserver is my homeserver that uses these VMs as “smarthost” and also pulls emails from there immediately. my mailclients are configured to connect to those VMs butbthat connection is relayed through VPN to my homeserver. thus i think my setup is a bit like what you want but i host everything by myself and i don’t use mailcow but it looks like i use the same software mailcow uses too. i guess you are mainly bound to what mailcow offers when limiting yourself to it ;-)