Crash/restore renamed SSD system disk and emptied
Both the directories you lost indicate you should pretty much immediately boot to recovery and re-apply the OS version you had.

You can't trust any tools if frameworks are damaged and you can't trust the apps to fix things if they're compromised.


Boot to recovery and verify you have a good recovery (internet or otherwise) and have internet while in recovery.
Run Disk Utility (from recovery) to repair the drive until there are no errors.
Confirm your backup mounts while in recovery so you know you have a good backup before proceeding. Back anything up that's not good before proceeding.
Run the OS installer to write known good new /Applications and /Library - that will run migration after the blank /Application is run to copy over all the apps / users / settings you have.
Consider checking the install.log for errors and then test the machine to be sure you don't need to recover things from the backup.


Pretty clear case where you'll have to do this eventually - so I wouldn't waste time on not verifying your backup and not reinstalling a known good system. Trying to figure what happened will just delay getting a known good set of apps and frameworks re-installed - then you can look over what failed if you care to.

You can also make your Recovery HD on another computer if needed. 2008 MacPro likely can't internet recovery and any recovery will let you reinstall 10.11 but you may have to choose that if you can't just install the latest OS your hardware supports.