HA ios notification works... kind of

I created an automation which sends a message to my iOS device (iOS 16.6). When I test it, the phone dings and the badge with the message shows up. If the notifications are set to temporary, the badge vanishes after a few seconds. If it is set to permanent, the badge stays there until I touch it (either intentionally or accidentally).

But, I don’t see the badge ever drop into the notification center like other notifications. For example, if the notification is set to temporary and I happen to not see it, it vanishes and appears to be completely gone, as if it never happened. What if I hear the ding from across the room and walk over to my phone. It’s totally likely that the badge will have timed out and vanished.

Normally, I swipe to the notification center and see what I missed. But the HA notifications seem to not go in there. They are ethereal, like a ghost. If you see it, you are lucky.

Is there some special trick to making the HA notification appear in the notification center?