Ordinary notifications obey the mute switch and whichever Focus is running. Critical alerts do not. They are the category Apple created for things like medical alarms and safety warnings, where staying quiet is the wrong outcome.
Two gates control them, which is why so few apps have them.
Apple's gate. A developer has to request the critical alerts entitlement from Apple and explain why the app needs it. Apps that cannot justify it do not get it, so this is not a setting an app can simply switch on.
Your gate. Even with the entitlement, the app has to ask you, and iOS shows a separate prompt for it the first time. You can change your mind later at Settings > Notifications > (the app) > Critical Alerts. Turning it off leaves the app's ordinary notifications working and silences the part that overrides the ringer.
Checked on iOS 18. If an app tells you it can ring through Do Not Disturb and the Critical Alerts toggle in its notification settings is off, that is the reason nothing happens, and it is worth looking there before assuming the app is broken.
Android has no exact equivalent. The nearest thing is a notification channel configured to bypass silent mode and Do Not Disturb, which the user grants once.
How RingIt helps
RingIt uses critical alerts on iOS, which is the whole reason it can make a muted phone loud, and an alert channel that bypasses silent and Do Not Disturb on Android. The app asks for the permission during setup and points at it again from the home screen if it is missing, because without it the app is just another notification. It rings the phone and nothing more: no map, no last-seen address, and nothing at all if the phone is off or offline.
The overview is in the introduction to RingIt.