Hello B,
First of all, don't engage the PTO at 1/4 throttle. That will cause a "load stall" on many different riders.
The engine requires higher RPM to overcome the deck rotational starting load to get everything moving. Also, the higher engine RPM provides more charging system voltage and amperage to engage the electric PTO clutch quicker.
Of course, the PTO clutch air gap is important to prevent excessive clutch slippage and overheating. So, make sure it is within specs.
Maximum rated horsepower is determined at 3450-3600 RPM, not at idle.
Idle charging voltage on a machine like this is typically at 13.0V and minimal amperage to maintain only the battery.
When RPM is raised, the Voltage and Amperage climb up to be able to handle the additional electrical load of the PTO clutch and any lights that may be required for late evening or night mowing.
I don't have an exact specification chart for your machine, but a few simple tests with a multimeter and Amp clamp will confirm what I'm saying.