My wife picked up some debris and got a simple puncture.
no damage to sidewall, hole right in the tread.
We patched the hole with a plug and reinflated. Tested for leaks and it's solid. TPMS light is still on though
What do we do?
You are giving Mazda's TPMS system the benefit of the doubt that it actually monitors pressure in real time. Assuming your plug is holding up and there’s no slow leaking where it is below the minimum, don't worry about the light and just drive. It will go away when it wants too.