You don't need to delete anything. I was just explaining how Finder sync works.
The photos on your phone, which you synced from your computer, I must assume are still in a photo folder on your computer? Check to be sure.
If you go to Settings > Your Name, iCloud, Apple ID, iTunes & App Store > iCloud - Do you have Photos turned on? If you do, you don't really need to do anything more.
How do you backup your phone? Do you use iCloud backup, which automatically backs up your phone, when your plugged into charge and connected to Wifi?
If you do, setting up your new phone when you get from an iCloud backup is quite simple. Here is a link about how to do that --> Transfer data from your previous iOS device to your new iPhone, iPad, or iPod touch - Apple Support
In that link are three ways to restore the data from your phone to your new phone.