iMessage activation unsuccessful or waiting for activation

Solved. I faced similar issue as you mentioned and have similar setup in my iphone 13 ( one physical and one eSim but both of Airtel). In past three days I tried every solution available on internet resources including some from Apple, but none worked. Did network reset also several times. Contacted service provider Airtel visiting their store who were of no use. The spoke to their helpline and but were of no help as they said from their side all is okey and I need to go back to Apple only for solution. It was finally my own intuition that I felt something is amiss at Airtel only which is preventing my phone sending of activation system SMS( which is necessary for activation of iMessages, FaceTime). Since I had not moved out of my location much for past few days, I went out few miles away so that Airtel Tower for my connection changes. It immediately worked and I could see on screen my phone sending system sms for activation and lo... it worked. Airtel must be having some issue that the Tower I was connecting to earlier from my home was preventing outgoing system SMS which are must for activation of iMessage and FaceTime. As the Tower changed it worked. This is my reading.