Or maybe... FastMail created JMAP, ergo they are the one with the best implementation.
Now Apple is working on moving iCloud to JMAP, and are working with FastMail as a JMAP production level service within mail.app.
Apple uses a proprietary IMAP extension that, until recently, any developer could use by generating a APNS certificate using a reverse engineered endpoint from macOS Server. They’ve since closed this.
How iOS Mail gets push inbox updates working with third-party IMAP servers is in the public since 2015/2016 if you look hard enough. That has nothing to do with JMAP the protocol inherently.
Fastmail have had sanctioned access from Apple (via their own APNS topic ID) - https://www.fastmail.com/blog/push-email-now-available-in-io...