how to do a full backup without phone

Odds are, if your screen is not working.. that you will not be able to perform a backup.

If you've backed up to a computer before, you could try plugging it in to see if it's recognized.. but you typically need to unlock the phone or trust the device, which requires interaction on the iPhone screen.

If you already had iCloud backup going, then it's possible that it would soon do another backup if connected to your WiFi network and plugged in. Of course, if you have iCloud backups going, you would only lose a day or so of stuff anyways.

If you've never backed up your phone before, then this will be a 'wake up' call for you. Backups are meant for situations like you are in right now and they need to be proactive, not reactive.

No. It’s too late for that. You need to back it up before something goes catastrophically wrong, not after.