Error 4013 (iphone X Repair)

I took in Iphone X to the Apple Store in Houston recently as it had suddenly started getting stuck on the 'Connect to ITunes' screen. Before going to the store, I connected it to my MacBook laptop to restore the phone and got error message 4013 'Phone unable to restore or update'. The associate at the store got the same message when trying to restore. My iphone is within the limited warranty period so sent it off for repair (repair ID R397800609). I received an email 3 days later from Apple saying that the engineers have found another problem that was not mentioned on the original request from the associate at the Apple Store. Also, some unclear photos of the inside of my phone were attached, as well as there being NO explanation as to what the problem was. I was told the phone could be returned to me unrepaired, or fixed for '$549 plus tax'. I am very disappointed and don't understand how this fault could have just suddenly arisen. I have $651 remaining on my installments with AT&T for this phone. I see online that there are companies that provide a service to fix 'Error 4013' with a software download for around $100. If this is an available option, why are Apple requesting $549 to fix this error? I'm an Apple-devoted customer who has always owned an iphone since the very first model. I also own a MacBook Pro, an Apple Watch, and an iPad.

I am currently using my old iPhone 6 Plus as a replacement phone.

Are there any other options I could explore or be offered that won't break the bank?

I now know that I shall be insuring my iphone from now on, which I wish I had done from the beginning.

Thanks for your help. Martin Proll. (Cell 281-687-4351)