The My Number field doesn’t actually change the phone number assigned to the SIM/eSIM. Since Sky transferred your number and the new one won’t save there, I’d first ask Sky to confirm that the number port has fully completed and that the eSIM is provisioned with the correct number.
Once they confirm that, go to Settings > Apps > Messages, turn iMessage off and back on once, then check Send & Receive. Your transferred number should eventually appear there and be selectable. Do the same check under Settings > Apps > FaceTime.
Apple says carrier verification of a phone number for iMessage can take up to 24 hours. If it still shows the temporary/old number after that, I’d go back to Sky rather than deleting the eSIM or changing your Apple Account settings.
→ Apple Support – iMessage and FaceTime activation