Push notifications get lost?

Is it me or do push notifications to an iOS device sort of get lost?
I mean in the sense they appear on my homescreen as popups but say you have five, don’t expand them out and just unlock your phone you can’t then get back to see them without going back into notification centre?

Should they not somehow appear with the red dot counter on the app which you can then go in and read?

Early adopter to HASS and used to Domoticz with pushover so tempted back to pushover as they both appear on the screen and I can also go back and see a list of alerts.

I think this is the way you set them up. I saw ‘badge’ as separate option in documentation.

Ok found the documentation for this properly Introduction | Home Assistant Companion Docs (home-assistant.io) but badge just seems to allow you to set a number, say 5.

It adds 5 on the app icon but nothing else so not sure the point of that.
What I did find poking through that is very useful ability to override the the DND and physical mute switch.

but still back to the point… it seems notifications get sent but only appear in notification centre rather than the app.

There’s a really clunky way around this, where I set up a notification to send an iOS alert as well as a persistent notification so when you go in the app there’s something to read and dismiss but surely there’s a better way than this?