Unable to register mobile number with apple account

Are you saying you can send and receive iMessages with your Phone Number, but FaceTime only with the Apple ID?

Turn both services off and reset activation

To activate iMessage and FaceTime using your Phone number

1. First, check to know whether you have an SMS plan enabled for at least one SMS*** with your carrier. Contact your Carrier (Cellular Service Provider), the agency that issued the SIM to you
2. If your iPhone is used with a carrier not found in the wireless carrier articles, make sure you can send and receive international SMS. (One international SMS*** Only)
3. If you can't turn on or sign in to iMessage or FaceTime - Apple ...

*** You may not have an SMS plan (Domestic & International) enabled by your carrier for the SIM/eSIM that you use on your device. Apple Inc. does not provide SMS services.

iMessage (Blue) -

• iPhone to iPhone: requires internet (Either over WiFi or Cellular Service) as it is sent over internet protocol. Needs Activation on your device.
• iPhone to Android: Not available

SMS/MMS (Green) -

• iPhone to Android: does not require any internet, it is sent over cellular voice protocol. Needs to be enabled by your Carrier for the SIM used by you.
• iPhone to iPhone: When iMessage is not activated or the device is not connected to the internet either over cellular or WiFi
• You need to have an SMS/MMS plan enabled by your carrier for the SIM/eSIM that you use on your device. Apple Inc. does not provide SMS/MMS services.