Well the diode measure on the meter for base to collector/emitter looks OK, as it is an NPN transistor, and PN junctions are diodes with about 0.6 - 0.7V when in forward bias.
It depends on your meter what it is really measuring, and I’m not sure what it would say collector to emitter (as it is really an open circuit). The collector to emitter showing 0.9 V is a bit suspect and maybe means the transistor is blown.
When in the circuit and the Arduino pin high and 0.7V on the base what is the voltage at the collector (should be 0.3 to 1V depending on current through the piezo)? Also when the Arduino pin is low what is the voltage on the collector (should be 12V)? If in the off state the voltage is much less than 12V, then yes your transistor is toast.