Windows Sees My Controller But It Sends No Input At All, Every Button Is Dead

Your reasoning is right and this is a genuinely interesting failure mode rather than just a cheap pad being cheap.

When a USB device enumerates, it hands the host a descriptor that declares what it is and what it will report. Your pad declares 12 buttons and 6 axes, Windows believes it, and the browser faithfully shows you 12 buttons and 6 axes. None of that proves the pad is actually sending anything, only that it said it would. The two common reasons for a clean enumeration with dead inputs are both at this layer.

The first is a mode switch. Many generic pads have an Analog or Digital toggle, often a physical button marked Mode or Analog with an indicator light. In the wrong mode the pad sends its data in a different arrangement than the descriptor it presented, so the host reads the fields it was told about and finds nothing in them. Pressing that button usually brings everything to life instantly, and it is the most likely answer for your pad.

The second is more common on clone hardware than people realise. That vendor ID 0079 belongs to a widely cloned controller chipset, and clone firmware frequently copies a descriptor from the controller it is imitating without implementing all of it. The host reads fields that the device never populates, and you get exactly your symptom. If the mode button does not fix it, this is probably what you have, and no driver will resolve it, because the device is misreporting itself.

One worthwhile check either way: open joy.cpl and watch the inputs there while pressing buttons. If joy.cpl is also dead, it is the device. If joy.cpl responds and only the browser is dead, that is a different and much rarer problem and worth telling us about.