Do helicopters have automatic tail rotor compensation for anti-spin?
Autopilots control the flight path, they usually concern themselves with the travel of the centre of gravity of the aircraft. Stabilising the aircraft is more the job of the human pilot. In a helicopter that is indeed not an easy job - larger helicopters have a mechanical mixer that helps the human do that, a set of lever arms that input extra tail rotor as collective is applied, for some automatic compensation of the increased torque of the main rotor.

Having to indefinitely put pressure on a flight control is an annoying issue for fixed wing pilots as well, that is why they can be trimmed. Stick and pedal forces can be trimmed away, so that the neutral point of the control becomes the point of zero force: once the control is trimmed, you can take your hands or feet off of it and it stays there.

In fixed wing aircraft, trim is usually adjusted with a flick switch on the handle. Flick it sideways and the roll control spring neutral point moves, flick it forwards and the pitch spring neutral point adjusts. Helicopters have such a switch as well, and that works well for fine control in cruise. But in the hover there is a lot of swishing action of all flying controls, and the beep trim switch is just too slow to follow this. Spring forces that are normally helpful, are now a hindrance.

That is why helicopters in addition have a trim on/off button: when selected, all feel forces cancel and the stick or pedal is very light, only a bit of friction and damping. What happens is that the feel forces neutral point automatically follows the stick position. Once the helicopter is stable, the trim forces can be selected ON again, and hands and feel can be removed - although I believe this is never a good idea in a helicopter.