Mark I was concerned about this and went to a T-Mobile store a couple of days before my iPhone 15 arrived. They said if Apple does what they have done in the past, you will find directions on your phone and all with work smoothly.
That was my experience.
I expect Verizon or AT&T people will have a similar process.
For T-Mobile people below is what I did.
Sequence is important.
#1. Update your iPhone to the latest OS before you start
#2. If you have an Apple Watch, update it before you start
#3. If you have a Watch, Unpair the watch if asked do you want to retain the Celluar, say yes. That will be needed for your new Watch or you existing watch once it is connected to the ne iPhone.
#4. Backup your iPhone to iCloud. This is not required, but it does give you 2 independent options to transfer your phone data and watch data if applicable.
#5. Turn your watch OFF – this is very important if you have a new watch also. Any watch that is not Off will communicate with any iPhone that is On and that can only run down batteries and confuse things.
#6. Turn On the new iPhone
At this point you will be following directions which will display on the iPhones. After you finish with your new phone, you need to “Pair” you watch with the new iPhone. After Pairing, you need to restore from the backup made in step #3 above.
During the process you will be given the option to restore your data via iPhone to iPhone Bluetooth transfer or from the iCloud backup. I used iPhone to iPhone Bluetooth and recommend that option.
During the Bluetooth process you will be told you need to update the new iPhone’s iOS to a new version or you must revert to restoring from iCloud.
After that everything is clear & logical - again following the instructions on the iPhone.
At the end of the process it is important to have old hardware (iPhone and Watch) turned off. Running a Lithium battery down to zero is the worst thing for the battery without destruction.
Process to turn off iPhones -
Quickly Press & release the Volume Up botton, Press & release the Volume Down button Press & Hold the power button until the turn off slider appears. Release the power button and turn off with the slider.
I found the WatchOS 10 process awkward - probably my arthritic fingers on the small screen – it is very different from the WatchOS 9 process. So figure it out before you start.