My small town has no alarm that sounds throughout neighborhoods. The only way the town notifies residents of a storm is by phone, and everyone who is signed up supposedly gets a call. The last time there was a tornado warning on TV for my area, I got no call from the City until one hour later, and that's not the first time they were late, so I have no confidence in them.
However, I check the weather forecast daily and each evening. If strong storms are forecast, I may "star" the City alarm as a contact; otherwise only immediate family members are starred. At bedtime, I set the phone to DND and my phone only rings if I get a starred contact call.
All other phone notifications are turned off. If I got an amber alert about a missing child, it would probably keep me awake for hours, but the chance of me having any helpful information is zero, so it is not necessary for me to get those alerts.
I have smoke and water alarms in the event of fire or water leaks, and security cameras I can view if I hear any suspicious activity outside in the night.