My wife has a new pixel phone and I am not able to get it to receive notifications. It is able to communicate with the hub but does net receive notifications.
Gary
In More > App Settings you can verify which Hub and "Device" it is connected it. Make sure that is what you are expecting.
Then first thing I would try is delete the app and reinstall it, especially if you moved it to the new device via a backup transfer.
Did you create a new "phone" device on your hub, or did you tell the phone app to replace one of the existing phones when you ran it for the first time?. Did you even see the option to replace an existing device when you first connected with the new phone?
Are you able to communicate with the hub both locally (over Wi-Fi) and remotely (over cell data) with the new Pixel?
Local communication is direct from the phone, to the hub. Remote "communication" and "notifications" require communications with the Hubitat web server.
I had the same issues with a new iPhone. It seems if your new phone has the same device name, it appears to be a notification device in Hubitat, but you should remove it and add it again. This fixed me right up.