I understand from Wikipedia that, "The length of the day, which has increased over the long term of Earth's history due to tidal effects, ...". If the angular velocity of the earth is decreasing then the stored rotational energy is decreasing. Where does the power/energy go?
You're correct in assuming the net angular momentum of the system in question here will remain constant. The Moon's orbit around Earth is responsible for the slowing of Earth's rotation. This effect is extremely small.
The decrease in Earth's angular momentum is transferred to the moon, which resultantly sees it's orbit accelerate. This acceleration also causes the moon to move further and further from the Earth. This trend will continue until they reach a common speed.
Where does the power/energy go?
It goes into heating the Earth and the Moon. That heat in turn spreads out into the universe.
While the Earth-Moon system comes very close to conserving angular momentum, it does not conserve mechanical energy. In fact, that angular momentum transfers from the Earth's rotation to the Moon's orbit means that the total mechanical energy of the Earth-Moon system is necessarily reduced. Mechanical energy is only conserved in isolated, non-dissipative systems. The tides in the Earth's oceans, in the Earth as a whole, and in the Moon as a whole means that the Earth-Moon system is dissipative.