I'm a Fenix 5 Plus user with a OnePlus 3T.
I noticed that my watch stopped getting notifications last week while working and waiting for a reply from a co-worker at a different location.
Then I noticed that the watch would randomly disconnect from my phone. Once re-connected, it would disconnect randomly again after an indeterminate amount of time, and that was when I noticed that my push notifications were not working at all.
Also, I am a (non-premium) spotify user, and the default music widget worked fine to control my music on my walks to work while I used my bluetooth headphones. When the aforementioned problems began, I also noticed that the music widget would not recognize that Spotify was running on my phone, and if I pressed the Play button, Google Music would boot up on my phone.
I tried every combination of resetting the watch, resetting and deleting data on the watch, removing Garmin Connect from my phone, forgetting the bluetooth settings for the Fenix 5 Plus on my phone, even removing the Fenix 5 Plus from my devices on Garmin Connect's website.
The solution that immediately remedied not getting push notifications or my watch not recognizing that Spotify was running:
Go to Settings -> Search Settings for "BTtestmode" -> force stop the application, reboot phone & watch, reconnect.
Hope this helps you folks with the same symptoms.