Opsgenie, the service rather than the mobile app, supports multiple notification paths. Rather than looking at the app, I think it makes more sense to look at the platform.
Consider using it alongside something like Pushover for better notifications. For example then you could utilise critical notifications and custom sounds, as well as vibrating on alert. Not affiliated, but I’ve usd Pushover for over a decade and it has worked flawlessly for my own triggered notifications.
In this case, just have it do it via email or API endpoint call, and define the notification details you want.
If you have to get authorisation to get the notifications routed like this., cite your use case, and extol that you are being conscientious and that you don’t want to miss critical notifications. The existing process has a known risk around that and you have a proposal to mitigate it.
Hope that helps.