Hi, James,
Thanks for visiting the Apple Support Communities. I understand from your post that the System category of your iPhone storage is taking up more space than expected, and you'd like to know what options you have to help manage what is on your device. I'm happy to help!
The "System" category on your device include the iOS software itself, as well as files supporting it. The amount of space required for the iOS and its supporting files depends on several factors (device type, model, country, carrier, Siri voices that you've downloaded, and even files that are too small to have their own category in storage) and will vary from device to device.
Restoring the device back to factory settings and not restoring a backup is a great way to remove files that have been mis-categorized as "System", or that were too small to be placed in a category of their own. Since the amount of space under "System" did not change on your device after doing this, it sounds to me like the iOS software and all the files needed to run your iPhone with your carrier in your country take up 6.3 GB of space.
While you can't directly manage what's stored in the "System" category, you can manage what is stored on your device using the tips in How to check the storage on your iPhone, iPad, and iPod touch - Apple Support.
Have a lovely weekend!