Another +1 for scrcpy, I've actually been in this exact situation before of having a functioning phone with a broken display/touchscreen, and was able to operate my phone through scrcpy until I got a replacement screen. Real lifesaver, amazing software.
True, but the chances of scrcpy being enabled on an Android device is limited and you also have to authenticate the computer connecting to the device from the device itself which most likely requires a touch screen. There may be a way to access the encrypted partition itself though using the hardware buttons, and then run a command to mount the encrypted partition.
The first thing you'll need is Google's platform tools, as well as a compatible ADB driver for your device if you're on Windows.
Then, you can use `adb pull` to copy data from the phone's filesystem to Windows.
Edit: another commenter rightly pointed out that this might not work when your phone is locked.
A quick search found some really interesting tools in this thread here (srcpy especially seems amazing!): https://stackoverflow.com/questions/29072501/how-to-unlock-a...