You control your own notifications from Settings, and email and push are managed separately.
These settings are personal to your account. Turning something off changes what you receive and affects nobody else, so you can adjust them freely without worrying about your colleagues or the people you coordinate.
The two lists are independent. Turning an email off does not turn the matching push off, which is useful if you would rather get shift reminders on your phone than in your inbox.
Push notifications only arrive through the mobile app. If you have never installed it, there is nothing to deliver them, and the settings will have no visible effect.
Your phone's own notification permissions also apply. If you denied notifications when you first opened the app, Vome's settings cannot override that, and you need to allow them in your device settings.
Most likely because you are a coordinator or a watcher on something.
Those are two different mechanisms. Notification settings control the categories of message you receive; being a coordinator or watcher on an opportunity, shift, form or sequence subscribes you to that thing specifically.
So if a particular opportunity keeps emailing you, the fix is usually to remove yourself as its watcher rather than to switch off a whole notification category. See What does it mean to be a 'Watcher' on Vome?
It is worth being selective rather than sweeping.
Shift reminders and approval notices are the ones people miss most once they are gone. If your inbox is the problem rather than the messages, turning off email and keeping push is usually a better trade than silencing both.