They're unrelated. With the bundle of unlimited energy, it has always basically wiped your existing balance and for x amount of time given you the ability to expend energy whereever you wanted to. The timed goal available for a few more hours still, has 2 offers of 10 minute unlimited energy and will keep your existing balance of energy once the timer expires. I did have to force close for the screen to come up. The area where your energy level is removed and it has the words UNLIMITED ENERGY with a countdown clock.
The goal unlimited energy starts as soon as you finish the related goal. You'll still need to sit through dialogue and congrats screens which eat into your time. I didn't like that at all. Hope that helps!