As a Proton Mail macOS user, when I'm waiting for an email, it's really annoying that I will get a push notification immediately on my phone, the have to hit refresh in the desktop client several times before the email shows up in the desktop client.

Perhaps https://protonmail.uservoice.com/forums/284483-proton-mail-calendar/suggestions/50545794-implement-push-imap-instant-email-notification is the right solution, but I don't really care how it works--I just want to receive notifications as fast on desktop as on my phone.