How can I access data on Charge Only mode (Phone's screen is non-functional!)?
There's little chance you can do that in normal system. But you can do it in (custom) recovery.

If you already have a custom recovery flashed, then skip this step. Boot it into fastboot (bootloader) and flash a custom recovery in.

Then boot into the recovery and you can access it using ADB shell. You can use adb pull to retrieve data from your phone.