New Garmin Lily SW version 10 paired with iOS 16. Notifications from email, messages, phone calls, and other apps are appearing just fine in the Notifications widget, but I do not receive any vibration or push notification when they arrive (so I don't know I'm receiving a call unless I specifically think to open the Notifications widget at that time).
I followed all the Manual and Troubleshooting instructions for enabling Persistent push notifications on my Lily and made sure to turn off Focus and Do Not Disturb modes, and I restarted my phone and temporarily connected the Lily to its charger to mimic turning it off and on.
Potentially related, notifications that were previously in my Notifications Widget will sometimes vanish, and sometimes resyncing the Lily or restarting the app will bring (at least some of them) back.
Let me know what info you need, and thanks in advance.
