What exactly does the extended energy bar for 799 diamonds give you?

You get 450 energy to start, energy that refills to 150 every 5 hours (instead of 110 in 3hr 20 min), and 150 energy (instead of 110) for every character puzzle you will complete and every star booster you will activate. It will remain a permanent feature of your game. Highly recommended for those who want to play more and need more energy for Detectives Needed Key Challenges or Team Competitions.