An OTA firmware update can change this behavior overnight. Unless it's a physical bounce switch that actually disconnects power mechanically, you are still at the mercy of someone else.
Looks like when you press the mute button, you both light the led up and pull-up the transistor gate (It looks like PNP so, it turns off when you apply power to the gate). This effectively cuts off power from the mic itself.
So, the LED is not controlled by firmware but, by the behavior of the circuit.
AFAIK, OTA updates cannot re-wire PCBs or do we have nanobots now?
[0]: https://1.bp.blogspot.com/-vVhoXpEtTXo/X_0iLmz9gcI/AAAAAAAAB...
That's literally what you're looking at.
The schmitt-trigger and the DFFs debounce the switch in hardware, and then the FET that controls the power input to the microphone also controls the power input to the LED. What do you want, a relay?
Firmware can only reset the DFFs (which does turn on the microphone), but it can't change the physically coupled LED / mic-power behavior.
Not as good as a physical switch I guess, but better than some implementations of laptop webcam activity lights at least...