Hi whyoga,
The first area to check for this concern is how the notifications for Mail are configured. Manage notifications from Mail on Mac outlines how to do so:
"Change or turn off all notifications from Mail
- On your Mac, choose Apple menu > System Settings, then click Notifications in the sidebar. (You may need to scroll down.)
- Go to Application Notifications on the right, click Mail, then do any of the following:
- Change notifications: Set options, such as the style of notifications, where to show them, and more. For more information about the options, click the Help button in the bottom-right corner.
- Turn off all notifications from Mail: Turn Allow Notifications off.
Note: To display notifications from Mail when a Focus is on, you must allow the notifications to appear. See Set up a Focus."
If those are enabled, the next place to look is possible Focus settings, as described in the previous set of directions.
Still not working? Test in safe mode per How to use safe mode on your Mac and then complete the recommended steps in that article based on the result of the test.
Regards.