Why is the piezo buzzer not making any sound?
Both the code and the circuit have problems.

In the code:

• If the while (buttonState == LOW) loop is ever entered, it will never be left, because buttonState, the controlling variable, does not change within the loop.

The simplest fix is to remove the line bool buttonState = digitalRead(buttonPin); and replace while (buttonState == LOW) with while (!digitalRead(buttonPin)), which says to loop while digitalRead(buttonPin) is not true; ie, while it is false, or low.

• The empty braces, { } at the end of the while loop are superfluous and should be deleted. 

In the circuit diagram:

• Neither of the leads of the buzzer is attached to the Arduino circuit, so it won't make any sound.  Note, tone(12,260); tells the Arduino to use pin 12 for tone output.

To fix this problem, run a wire from pin 12 to one side of the buzzer, and a wire to ground for the other side of the buzzer.

• A blue LED in series with a red LED might or might not turn on when supplied with 5 V.  For example, if the red LED takes 1.8 V and the blue LED takes 3.3 V to turn on, the 5.1 V total is too high to be turned on by 5 V signals.  Remove one of the two LEDs, and move the wires to the other LED to complete a circuit.