What's the purpose of these copper coils with resistors inside them in A Yamaha RX-V396RDS amplifier?

Emitter Followers are prone to oscillation with capacitive loading with unity gain and so are complimentary Darlingtons emitter followers in a feedback loop used in PA's. Normally PA's use series with RC shunt snubbers to suppress absorb spurious RF oscillations > 100kHz to dampen them at the unity gain BW frequency of the power amp.

However, Yamaha, being the expert in Audio design that they are, prefer to raise the output impedance with leading current phase compensation using these series 1uH inductor coils shunted by a 10 Ohm resistor. This provides a breakpoint or HPF or phase compensator at 100kHz where the PA source impedance rises from milliohms to 10 Ohms and thus prevents the oscillation with phase margin.

The trick however, is to make them a high Q vertical axis low capacitance air coils so they have a very high self-resonant frequency and also by orientation, do not couple each other in the 5 power Amp channels on the same board. Only the best designers use this approach.

The coil can be found in service manual schematics. It is an RL filter to isolate the amplifier output circuitry from the speaker terminals.