I am experiencing the same issue only with iOS 18.2 and iPadOS 18.2. I have iCloud, Outlook, and Exchange configured, with notifications set to Lock Screen, Notification Center, and Banners. "Customize Notifications" is set to "All Unread Messages," and all accounts are configured for Alerts and Badges. I’ve also tried "All Mail" and switching to List View in the Mail app.
The badges and banners display as expected when my phone is unlocked. However, when locked, I either sometimes see mail notices in the Notification Center, not at all, or with a delay of several hours. I’ve verified that Notification Center is enabled on the Lock Screen.
I reported this as a bug. It’s frustrating because, as a system engineer, I depend on timely mail notifications to monitor critical application processes.