Thanks! 
Your example helped me further! GPIO2 seems to be the kind of a pin that needs a sudden pulse (that the pushbutton sends), not continuous current as coming through PIR sensor during 2 seconds. When I boot the system with the PIR sensor data wire disconnected, touch the PIR sensor and then in 2 seconds “hit” the GPIO2 pin with the jumper wire’s metal head, the ESP32-C3 awakes from deep sleep and the LED starts blinking.
My setup:
