Velocity is constant when Thrust = Drag
The purpose of any propulsion system is to produce thrust.
why talk of power with props?
This is a "left-over" from a time when early engineers, such as the Wright Brothers, put a propeller$^1$ on to any engine available to attempt flight. Engines are rated in "horse power".
Power is Force × distance/time
With the aviation propeller application, the power of the engine is absorbed by the drag torque of the prop: drag force x the distance from the center of the prop shaft$^2$
This definition can lead to some very embarrassing observations because:
Thrust is a function of power and propeller efficiency
A 2000 Horsepower engine can be churning away without producing any thrust if the propeller efficiency is 0.
The full equation for propeller thrust is therefor:
Thrust is proportional to (Prop drag torque) × prop efficiency
Since "power required" = "prop drag torque" ("power" is directly translatable to "throttle setting"), the usage has stuck, often as RPMs or % Power, but this only refers to power into turning the prop. Thrust output efficiency will vary with speed, especially for fixed pitch props.
variable pitch props have a far greater speed range of efficient thrust output until...
Pitch to maintin optimal prop AoA to the relative wind
becomes too great
Incoming air velocity into the prop disk gets closer and
closer to the exit velocity
This is why prop driven planes max out at around 400 knots, even with huge power plants and variable pitch props.
so how do you know how much thrust a propeller is producing?
By calculating the angle of dive in a glide for a given airspeed and multiplying the sine of this angle × the airplane weight.
This is now the thrust force required for level flight (for that particular aircraft).
If you want to know your thrust at full power and a lower airspeed, add sine angle of climb to your value.
Doing this, and plotting data points, can give some very good thrust data for a given aircraft/engine/prop combination.
and, of course, one can try various props for climbing or cruising needs.
$^1$ it should be noted that the Wright Brothers did make considerable progress in improving propeller efficiency.
$^2$ this can be 1:1 with engine crankshaft or it can be geared