The 1000 uses 2 BT connections, “Edge 1000” and a “BT_1000” (or something similarly named). The BLE is the low energy and the part that allows notifications. Make sure that is running in the iPhone BT configuration.
Note that that there have been a lot of issues in the past 2 iOS releases with Garmins and they have not fixed, even with new software released last week. My 1000 would not automatically make the BLE connection after the past Garmin OS update, I had to do a manual connection. This is the case as well on my 1030 which sometimes will not connect at all. Hoping Garmin gets all this fixed but in truth I’m think they are not committing the resources as the abated issues go back a few years and was one of the things DCRainmaker commented on (Livetrack) when he called out Garmin on this a few months ago.