If you are racing at stop lights, towing, or other activities you may need every edge you can get and need premium in a turbo.
But octane has nothing to do with energy in the gas. Yes timing will make a slight difference in power but not noticeable by most people in day to day driving.
Optimal mpg will require premium in a turbo, but unlikely economical.
If the computers and sensors are working I would not worry about hurting the engine
regular gas is likely most economical and a good choice most of the time and most people will still be happy with the performance. Heck I'm happy with my naturally aspirated v6.