If you want to use MT devices 24x7 they must have at least one live gateway MR/MV device in range 24x7, so you need your physical+logical network design to meet that requirement i.e. if you want to power down switches etc., they can't be the ones in the sensor-Dashboard communication path.
The automations you mention are two distinct topics...
i) can you control MT40 downstream power via the API?
Yes, using these...
https://developer.cisco.com/meraki/api-v1/create-device-sensor-command/
https://developer.cisco.com/meraki/api-v1/get-device-sensor-command/
For just APs, you can also control PoE via the API.
ii) you need somewhere you can receive a webhook from the MT30 to trigger i)
This is the part you need to develop, host and secure.
Bear in mind, the button is stateless, i.e. you can use it as an on/off switch, but unless you can independently determine the current power state, you cannot predict whether pressing the button will turn things 'on' or 'off'.
A simple workaround would be to use two buttons, one for 'on', one for 'off', though this still leaves the actual pre-press state unknown without independent verification.
Of course if the button is 'local' to the switches, then the verification issue goes away and you could use one button, but then why not just use a power switch.
Also, I'd want a protective cover for the button(s), things get pressed by mistake, it's only a matter of time 🙂
