The Bluetooth functionality of Stryd is always on, meaning that you can pair it with your phone, Suunto or Polar watch at any time even when Stryd is not in use.
However, if Stryd is not detecting motion, it will go in to an energy saving mode to save battery power. The accelerometer sensors and other functionality is switched off. Only after moving for 30 seconds or so, Stryd will reactivate and start transmitting power and other data.