Comment by prmoustache

The IMAP protocol has an IMAP IDLE extension for that purpose.

But is that use case really common in practice? With chat tools people don't tend to use email for instant messaging (well, appart from deltachat users, which can be a solution too!) and my experience is that it doesn't even work like that / that well for office 365 users. I am regularly told on teams that an email has been sent to me (same org and same region) yet it still takes more than a couple of minutes to have it visible on my desktop outlook client.