A relay by definition does not send a signal. It simply opens and closes a circuit. Internally there’s a reed switch in there and if one side is open then the other side MUST be closed. It doesn’t make sense that both sides are open at the same time.
Disconnect grey, brown, and blue wires, then the put your multimeter on continuity tester mode. Verify that the multimeter is working by touching the two probes together, it should beep/light up indicating continuity.
Now touch the probes to the gray and brown leads (NC). The multimeter should beep indicating continuity. Next, touch the probes to the blue and brown leads (NO). The multimeter should not beep because this circuit is open.
Now, trigger the smoke alarm and repeat the tests. The results should be inverted while the alarm is active.
Please share your results!