(Does Bulwark work with non-Stalwart mail servers? Bulwark communicates via the JMAP protocol (RFC 8620). Any mail server that implements JMAP should work. However, Stalwart is the primary tested backend and offers the best integration, including calendar, contacts, admin panel, and plugin management support. You can also configure custom JMAP server endpoints directly from the login page."
IMAP meanwhile is still nearly universally supported, and there are many independent mail providers that will host your inbox for a low cost without being locked into paying Fastmail or running your own infrastructure.
That really does not seem like a workable solution. It would probably be brittle, require double the storage, require mapping of accounts and and credentials, would not account for caldav/carddav, etc.
If JMAP is to take off we need proper clients, servers and bridges. I'm not sure we even have one proper OSS implementation for each.