I would suggest you use a power source of 4.5-4.8V and not the 9v battery with the LDO.
You can do that with AAA batterys 4*1.2v or 3*1.5V .
"Switch" S as before.
you may need to recalculate the series resistor to the LED.
View attachment 23395

of course that still isn't going to work, as there is no voltage to the S pin to turn on the transistor
you still need to take a probe wire from the 4.5V to the S pin that can be tapped on and off to activate the relay
View attachment 23396
cheers
Dave