Restore data from iPhone with Restore Screen

I have an iPhone X. Yesterday suddenly the phone restarted by itself and this screen appeared.

Apple support said that this means that the operating system has broken down and needs to be reinstalled. However, this also means that the entire data on the iPhone will be wiped out. I have really important stuff in there that hasn’t been backed up on icloud <– 5GB of basic storage was insufficient. I know that I should have purchased more…

My question is, whether there is a way of recovering photos form the phone and documents from program Files before restoring the system?

I would very much appreciate any help!