Not getting any push notifications on iOS - remote access required?

I have purchased my first G5 Turret recently, it's connected to a Dream Machine Pro Max which has 2x 4TB of storage in it.

I generally really like how all of this works, but one thing annoys the hell out of me: I do not get any notifications on my iPhone for anything. I do get mails for all detections, that part works just fine. But even though I've got both the Unifi Network and Unifi Protect apps on my Phone (iPhone 16 Pro Max), I don't receive any app notifications.

It may be a relevant detail that I have remote access disabled. The whole point of using Unifi gear for me is that everything is local and I absolutely will not ever enable remote access to my Router - I'd rather throw all the Unifi gear out and buy Mikrotik than doing that.

Is there anything I might have missed, a configuration option I may have set up wrong, anything? I'm currently very interested in the G4 Doorbell Pro, but that would only make sense for me if I could get notified on my iPhone and Apple Watch.