If you have beta 13.2, then you'll need to wait for the final release of 13.2 on your new iPhone before you can use the backup from the old iPhone.
As I said, the iOS version on the new iPhone, needs to be the same or newer than whatever the beta version is on the old iPhone to use a backup from the old iPhone. So if the beta is 13.2 you need 13.2 or newer on the new iPhone.
Using the backup from the old iPhone on the new one will not delete anything on the old iPhone no.
You can of course, if you do not want to wait, install the beta on the new iPhone. But I strongly suggest you don't do this as its clear you are not ready to handle issues with the betas and as they are confidential cannot really be discussed here as such.
There's no point in erasing the old iPhone at this point. You'll just lose all your data and gain nothing. The best thing to do, is to remove the beta profile from the old iPhone so you don't keep getting beta updates and wait. Then when iOS 13.2 is released to the public update the new iPhone to it, and use the backup from the old iPhone to restore it.