In my experience, the random "SIM sent message" happens infrequently and is related to communication between SIM and network. This has nothing to do with iMessage, that is a separate pop-up.
You cannot feed the number manually because your
iPhone already has proper settings it needs to understand and work with Airtel.
If iMessage is not working on the 12 mini, please go to Settings > Messages and toggle iMessage OFF and back ON after a few seconds. You will get a pop-up to enable Facetime and iMessage, Accept it.
Another thing - ever since unlimited free calling and 100 free SMS, we do not have the need to have some amount of money as prepaid balance. Please recharge with some amount to get prepaid balance, and then you will be able to activate iMessage on the new device - that is because that activation process sends an International SMS costing INR 5 which you would not have in your prepaid balance today, generally speaking. It is advisable to recharge with INR 100, that will give you about INR 87 as balance. This balance will also come in handy when you want to call 1-800 or 1860 numbers (usually your bank call centres) as these are chargeable in Airtel and Vi both.
If you are wondering why is it that you might not have had to recharge for your Xr, that's because when you get a new number or when you port into Airtel, you get INR 5 as prepaid balance. The Xr would have consumed that and activated iMessage. Now, the 12 mini does not have any balance to use.