Backup iPhone with dead screen on unknown Mac

My grandma´s iPhone 6 dropped from about 6 foot height, and the screen is absolutely dead. The iPhone itself seems to not be dead, but it´s locked and shows no visual indication whatsoever. When pressing power button + volume down, I can force power it off. And using the power button, I can put it on again. I know that it´s on because the button vibrates upon "pressing" it (it´s vibration simulated). Some of the data on it is not backed up in iCloud, and we need it. Connecting it via Lightning to USB of a PC doesn´t do anything, nothing shows up in iTunes. I had the intuition that it might work better on a Mac. So how can I pair / connect it to a previously unknown MacOS system via cable without unlocking it? What can we do to save data that would be lost on the phone otherwise?