I have a 7+ and storage was full— 31GB out of 32GB used. Deleted everything I could— nothing helped. Couldn’t install the update (13.6.1) and didn’t have a device at home to connect to iTunes. Managed to fix the phone with these steps: Screenshot of apps as they appear in storage (or write them down if you can’t take a pic)
Deleted the largest apps so I had enough room for the software update.
Downloaded and installed the update. Still showed 31GB used so ...
Did a phone reset (settings>general >reset >reset all settings
Turned phone off then back on
Checked storage and now is 15GB used
Downloaded all the apps I had deleted (took only seconds) and checked storage—still showing only 15.6GB of 32GB used. Phone is working perfectly... for now at least :) Hope this helps someone!