Are gyroscopic effects of tail rotor noticeable with hover spot turns?
The tilt and the gyroscopic effect cause the helicopter to hover with a slight bank in a no-wind condition, a compromise that is acceptable. It should also be noted that a crosswind can exaggerate the bank, eliminate it, or even cause the helicopter to bank in the opposite direction.

In helicopters, the controls are rigged is such a way that when forward cyclic is applied, the helicopter moves forward, likewise for aft, etc.  To accomplish this, the pitch horn is offset 90º to the rotor blade.  The controls still tilt the swash plate in the same direction as the control input is made, but due to the pitch horn placement, the input to the blade occurs 90º earlier in the plane of rotation. The tail rotor as a gyroscope is rather insignificant

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Also,  speed decreases all the way from the start of the approach to the hover point, and the power, controlled by the collective-mounted throttle, decreases during the first half of the approach, and then increases during the latter half - as the helicopter nears the hover spot and loses translational lift.

In a stable, no-wind hover everything is in equilibrium. The engine is providing just enough power to keep the main rotor turning at just the right rpm to hold the height over the ground and to keep the tail rotor spinning at just the right angle to counteract the torque of the main rotor. When you push one or the other of the tail rotor pedals forward, you upset this balance and must do something to compensate in order to hold the same hover height.

In a hover, the torque of the main rotor tries to turn the fuselage to the right and therefore pressure on the left pedal is required to keep the nose straight. Forward left pedal means the tail rotor blades are biting the air at a greater angle of attack and therefore producing more lift. If you add even more forward left pedal to initiate a left hovering turn, you increase the tail rotor blade pitch angle even more. This requires more power from the main gearbox and, if engine power remains constant, the only way the gearbox can satisfy this increased demand for power from the tail rotor is to allow main rotor rpm to decrease.

The tail rotor provides horizontal thrust but only to the right (nose left).  The tail rotor counters the torque on the fuselage caused by the engine driving the main rotor