In the latest version of the iOS Gmail app released on June 4, they added a feature that allows users to choose to only receive notifications for "Important"/"Priority" emails. This option is only available to users that are using the "Important first" inbox or "Priority Inbox" in the web version of Gmail.
I'm using the "Important first" inbox. I chose to only send me iOS notifications for "Important only". However, I'm not getting notifications for all important emails. I know this because the badge for the Gmail app is updated correctly, but I don't get any lock screen notifications for all these emails. I get notifications for about 25% of all Important emails, and the rest I don't get notified.
I already tried deleting the app and reinstalling it, but that didn't work. Anyone know if this is a known bug of the app? I recall another bug where the app would continuously notify the user by sending notifications for the same email over and over again, until they deleted and reinstalled the app.