Hey I just did this for someone and didn't see it posted anywhere else on the internet so I figured I would share my knowledge here. Also it will be sloppy as I'm writing it before work.

This is a tut to backup local data from an android device that powers on but has no display or touch functionality. It assumes you know the pin or password to unlock the device. If you use swipe to unlock the device you're probably boned.

You will need a USB A to C adapter so you can plug USB devices into your phone
Preferably a USB/Bluetooth mouse keyboard combo or a USB keyboard, a Bluetooth keyboard and a Bluetooth mouse.
Usb drivers for your phone installed on a PC
Minimal adb/fastboot installed on PC
A working android device for reference is helpful as mileage will vary from device to device (I performed this on a Google Pixel 6a)
A little bit of patience as you will experience trial and error.

Power on device
Plug keyboard into phone
Press enter
Type pin or password
Press enter
Allow some time for phone to load and get past missed notifications if its been off for some time.
Turn volume up to max either with keyboard or side buttons if they are operational.
Press windows key
Type settings
Enter
Enter
Press down
Press up up up
Enter
Type TalkBack
Enter
Enter
Enter
Tab
Tab
Enter
Phone should start reading all text output on screen, this will remain on even with reboots now.

From there reboot the device and follow the same general steps to enable developer mode then USB debugging. Enable bluetooth and add your bluetooth keyboard and mouse now as you will not be able to use the usb peripherals while requesting debugging connection authorization and the adb backup request while connected to PC. I will finish writing that after work.

adb pull -a /sdcard C:\

 

[KleinesSinchen]

Hey I just did this for someone

Nice. Congratulations on succeeding with this!
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The actual steps might be a little different depending on the manufacturer. Having a working unit of the exact same model will make things a lot easier. As far as I know there was some button combo by default to turn on Talkback (for blind people there must be an easy way to enable the screenreader).

However, a few problems remain:
A phone/tablet won't simultaneously act as USB host (keyboard) and USB peripheral (MTP, ADB). To control the phone and accept debugging from a PC one must most likely switch to a Bluetooth keyboard (should be possible to perform the pairing once Talkback is active)

Using a Bluetooth keyboard right from the beginning requires that the keyboard is already paired to the phone and BT is already active on the phone (which one should normally avoid in my opinion. BT has huge attack surface and a bad track record regarding security).



Any method of accessing the data in case of broken screen, especially if the touch functionality is also broken, will fail on a properly secured Android device.
As always the best method to recover data is a good backup. I know it sounds cynical – still the truth.