Extracting data from a working iPhone without a functioning screen

Hello, I have an iPhone which has been dropped from which I wish to backup its data. The phone appears to be fully functional (it plays sounds and vibrates at appropriate times) except the screen remains completely blank at all times. I am also unsure whether touch inputs register with the phone, but hopefully poking at a black screen would be the very last resort before attempting to take it apart. I have all associated passwords for the phone. I believe the OS version is 13 or 14, and it has never been "paired" to any computer, nor does it "trust" any USB device. Is there a way to get the data without first fixing the screen?