The LED actually shares the GPIO pin with the button itself, intended to provide immediate feedback for the button and to use as few pins as we could get away with for the OnOff SHIM so it would work with as many HATs/pHATs as possible. Right before shutdown the provided scripts will also flash this LED to indicate a successful shutdown.
It can be controlled at runtime, but while the LED is being controlled the button cannot be read.
Shorting the button pads together (one is ground, and one is the power on/off signal connected to BCM 17) has exactly the same effect as pushing the built-in button.
You could easily deadbug an LED across the +5v or +3.3v pins and any available ground pin, with an appropriate resistor.
See https://pinout.xyz/pinout/onoff_shim for the layout of pins- bearing in mind Button SHIM covers the top 12.