Hi @Absiddiqi, let me see if I can help out here!
Do you receive any kind of error message when you try to open the rear camera or does the display just turn black?
In addition to the troubleshooting measures you mentioned, I would suggest that you try to repair the software on the phone using Xperia Companion and a computer. It is similar to a factory reset, the difference is that the factory reset only deletes user data from the phone while the software repair will also replace your current software with a new one. And as the software repair will erase all user data, it is advised to do a backup before the repair to avoid data loss.
If the software repair do not manage to improve the functionality of the camera, I believe that the best thing to do is to get in contact with your local support team in order to have your phone sent to an authorized service center. If you have any questions regarding the service such as service routines, warranty and consumer laws, these kind of questions are best answered by your local support team as well
I hope that helped!
