HomeKit takes advantage of the iOS 13 update by extending notification support to more accessories. They will be able to alert you through the usual iOS channels of different kinds of events. It is a little bit the basis for these smart home devices...
The release notes of this update mention several kinds of accessories that will alert you through the iOS "Home" app.
Another welcome improvement is the ability for HomeKit device to notify you when an update is available. For example when there is a firmware revision to apply.
The smart home brand Aqara, which has 20+ HomeKit devices in its smart home system, goes into the details of how this long-awaited innovation works. It provides notifications to the Aqara Door and Window sensor (which monitors the opening of a door or window) and Aqara human body sensor which signals a presence.
In the case of these two accessories (or equivalent in competing brands) the notifications are to be activated in the Apple Home app. Then their display is adjusted in the usual iOS settings.
An important detail highlighted by Aqara, notifications are sent directly from the accessory to your iOS device, through encrypted communication. Apple servers are not solicited as for other notifications. We can see a good thing in that.
The other side of the coin is that if you don't have a fourth-generation Apple TV or iPad (with iOS 13) to act as a smart home hub between the accessory and your iPhone when you're on the go, you won't get these notifications. To receive them, you must be within Bluetooth range of the accessory. Without being equipped with a captive foot, these notifications lose much of their interest.
Another resulting shortcoming is that Apple does not allow an accessory to condition the sending of a notification to your absence from home. As a result, if you don't want to receive any at all - every time you open your doors or windows equipped with detectors - you simply have to disable these notifications...