Using the HDMI out on the phone is the best option. If your phone doesn't support video out, this is the best way I found to do it.
I recently had to do this with my pixel when the screen died. I couldn't find this advice anywhere so I'm super proud of this work around. Unfortunately it's not easy. You'll need a OTG adapter, a wired keyboard, a Bluetooth keyboard, and a crap ton of patience.
Step two: connect the wired keyboard using the OTG adapter. Use the keyboard's keys to unlock the phone and use the arrow keys to navigate to the Bluetooth settings.
Step three: connect the Bluetooth keyboard to free up the USB port on the phone.
Step 4: use the Bluetooth keyboard to enable the backup method of your choice.
I just enabled (Android on Samsung phone) talk back while in bed late at night with sleeping partner.
Warning, lol:
Enabling this will change your phone's input IMMEDIATELY and it will start making a LOT of sound that you cannot mute entirely.
You select sections by tapping on them and the system will read them out to you, but to actually press them, you double tap the screen elsewhere. It will literally say double tap to activate, but I immediately turned my volume down as low as it could go and couldn't hear it and started getting scared/frustrated that the entire input method of my phone changed and was out of control. I couldn't even unlock my phone normally, and luckily had my face recognition enabled and screen bright enough to illuminate my face.
So yeah, turning on the feature was a face first adventure. I'll mess with it later because it seems cool, but....lol be aware.
also upon being able to attack external screen one probably could attach external keyboard and mouse. use those then to operate the device. Depends on exact phone of course, but often android phones accept external keyboard and mice.
Yes! If you replace the broken screen with a working one, you'll be able to see the interface, and then you can enable USB file transfer as you would normally.