Thank you @Andrea_Mayer. 
To me, the answer is “You can’t recover projects in the Asana App UI.”. They removed the feature that has been there for 6+ years, adding additional manual work for the customer(us) and their support team, increasing the recovery time. Bad solution.
The optional solution of backups doesn’t provide the option to recover, just recreate an object, which makes a big difference as all timestamps and user history is lost or not stored in the default Asana data object structure.