How can I back up my phone when it won’t power on?

I think you already know the answer to this one. You can't.

Try a Forced Restart. Follow the instructions very carefully.

Force restart iPhone - Apple Support

There are 2 possible results:

1) The phone returns to normal operation

2) There is a hardware problem on the phone that will need attention at the Apple Store or Apple Service shop

Put it on charge for at least half an hour, then, keeping it plugged in, try a forced restart of your 14, using these gestures:

Press and quickly release the volume up button, press and quickly release the volume down button, then press and hold the top (power) button. Only when the Apple logo appears (it might take 10-20 seconds), release that button (ignore all other screens that might appear, the one with the "slider" to turn the device off included).

If the issue persists, contact Apple Support directly, using this link:--> Contact Apple for support and service

Regards

Giulio