Complicated Back Up

@steve359 is correct. However, it can sometimes be very difficult to get video onto an external display. If you connect an external display, but nothing appears, then I would attempt to blindly log into macOS by typing the first character of a macOS user account followed by the "Return" key which will bring up the password field for that account. Enter the password and press the "Return" key to submit the password. If you have more than one user account which begins with the same character, then you will need to try a password for each one. Just make sure to give the Mac enough time to reach the login screen. I'm assuming you have a list of users on the login screen. If you successfully log in, then video should appear on the external display.

The other option is to use Clamshell mode which requires you to connect the charger, the external display, and a USB keyboard & mouse. Power on the laptop and immediately close the lid to see if the video will default to the external display. Sometimes you may need to close the display immediately after the startup chime. Sometimes Clamshell Mode is hard to get working.

If you have another Mac, then you can try putting the laptop into Target Disk Mode in order to allow the other Mac to see the data on the broken Mac. If you have an M1 Mac, then this won't be an option without a working display.

You should always have frequent and regular backups of your computer and all external media (including the cloud) which contains important & unique data. You should do the backups before any problems arise. Waiting until a problem occurs may result in data loss.

Try plugging in an external monitor. Unless the entire display circuit path is broken there is a good chance it will work.