We are looking at a propeller aircraft and we must equate for two different animals. Power = Force X Velocity (Thrust X TAS)
For the Jet aircraft, all performance considerations come back to Thrust, except in the ABSTRACT sense in evaluating Rate of Climb by comparing Thrust X TAS at varying speeds. Because (for the jet) Power increases with increasing speed, best Rate of Climb speed is very high, often in EXCESS of the cruise speed to follow the climb. The opposite is true for the propeller aircraft.
The best Angle of Climb occurs at a speed where there is Maximum Excess Thrust. This speed is, for PRACTICAL purposes, Vmd. Best Angle speed is somewhat less than the normal En-Route Climb speed.
The best Rate of Climb occurs at a speed where there is Maximum Excess Power. As jet engines directly produce Thrust, not Power, it is necessary to consider Thrust multiplied by speed (Power = Force X Velocity). Thus, for a given Thrust setting, Power increases as TAS increases. Thrust actually ‘dips’ as speed increases, but then there is significant Ram recovery at higher Mach Numbers, thus further increasing Power at higher speeds.