Where are my iPhone Messages notifications? Recently I've noticed that I have no notifications (no badge, no bubbles) for SMS/iMessage in my iPhone. I have the following settings:  


Notifications: allow, show in notification centre, sounds - note, badge app icon, show on lock screen;  
Messages: iMessage, text message forwarding - my iPad, my MacBook - all off, send and receive - my phone and email;  
Do not disturb - off.


For me this looks like a serious bug (in 9.3.5?) or a security issue, but since I've checked text message forwarding I don't know how it could be.  

What else to check or how to fix this?
Often a hard reset of the device will fix problems. Powering off and back on doesn't do the same thing as it does for a computer - it's more akin to hibernate mode in that its drawing no power, but nothing (RAM etc) is cleared.

To do a hard reset, on iPhone 6s and below, press and hold Sleep and Home until the Apple logo appears. On iPhone 7 and higher, press and hold Volume Down and Home.