About constant speed props and commercial maneuvers

I asked this question to my CFI, but he just give me a blank stare, so
I'm hoping someone here could answer it.

As I understand it, all commercial maneuvers revolve around the idea of
converting between potential energy and kinetic energy, and the control
characteristics of the plane assiciated with these conversions.

Think about a lazy eight without the turn, to keep it simple. You're
just keeping a constant power setting and climbing then descending.
Before you start the climb you are cruising at 100 knots at 3000ft.
High kinetic energy, (relatively) low potential energy. At the top of
the climb you are now at 60 knots (low kinetic energy) and 3600 ft
(high potential energy). Now if you were to let go of the controls, the
plane will naturally nose down (if you trimmed it right) and level back
off at 3000 ft, and at the starting airspeed of 100 kts too.

The reason for this is the laws of thermodynamics. Energy converted
back and forth always equals the same in the end, with a small loss due
to entropy.

Now with that all said, imagine how a constant speed prop will perform
diffrently than a constant pitch prop. I don't know much about constant
speed props much since I've never flown one. When your airspeed
decreases in a constant pitch prop, engine RPM decreases, therefore
horepower decreases, right? But in a constant speed prop, the prop
governer will decrease the blade AOA, keeping the engine RPM the same,
but will horsepower remain the same? Would this result in less total
energy lost across the airspeed changes, therefore making it easier to
do commercial maneuvers?