Oh, Gmail's IMAP IDLE is far from perfect.
In fact, incomplete, it does not send message flag changes (known since 2007, no plans to fix on Google's part).
Aqua has a workaround for it. You'll see message flags (read/unread) update up to 10 minutes late, but at least they will update.
Overall, I'd place Cyrus / Fastmail first, Dovecot second, and Gmail somewhere among the other services with their own IMAP server implementation, but not at the top of that respective section.