Apple does sell refurbished 13 Pros, they just don’t have any in stock at the moment. It sounds like you bought a broken and used iPhone 13 Pro that looks okay, but I definitely would not consider it refurbished.
I would return it – you’ll need to enter a passcode any time you unlock the phone, open certain apps, using Apple Pay, etc. Face ID is essentially seamless in use and you would be missing out on the actual ease of using an iPhone with Face ID.
Honestly, if you actually want to put your phone camera to its full potential, you need to shoot in ProRaw and edit the raw image in an app like Lightroom. At minimum, 50% of photography is the process of editing photos to get the result you want – a lot of photographers like to say that they make pictures, not just take pictures.
There are apps like Halide that will allow you to play around with the ISO, shutter speed, aperture, etc. But adjusting the brightness by sliding your finger up and down using the stock camera app, tapping where to zoom, getting a bit of bokeh, etc. on an iPhone is doing essentially the same thing in a less-technical and more user-friendly way.
I know you say your friend has been able to take “mean shots… bone stock” with his S22, but keep in mind that even if he’s not using software like Lightroom, Samsung Galaxy cameras (along with all digital cameras) process jpegs in their own way that still has an impact on the end result that is still slightly “edited” from the actual image that was captured.
Anyway, if you want to make a good photo, the subject, composition, and lighting are honestly more important than whatever camera or app you use.