I got an iPhone 15 to replace my iPhone 13. I had problems during the transfer and needed the recovery key

I bought an iPhone 15 Pro to replace my 13 Pro. The transfer did not go smoothly and I was stuck at a point not knowing what to do. So, I went to the T-Mobile store (which was a mistake) and they caused me more problems by creating a new Apple Email account. They did get my phone number transferred and working. But, I had no access to the iCloud backup for my previous account.

I have installed iCloud on my Windows 11 desktop computer and the iCloud backup data is there. It is using my original Email address and not the one T-Mobile created. I have logged out of both phones and logged into the iPhone 15 with my original Email address. It shows that my iCloud backup is there. So, the bottom line is how is the best way to get that backup onto my iPhone 15? I am not sure as this is new to me. It seems there are two methods. One, using the phone to restore the backup requires me to erase all content and setting on the phone (which makes me a little nervous and will I have access to restore the backup)? The other is to use the backup on my computer through a USB cable. I am leaning toward this method as it seems simpler but would like.

Any thoughts or suggestions greatly appreciated.

Thank You

Bill