A Zener diode has three datasheet values to consider; one, is a package-related power limit; second, a recommended bias current. Third, is the dynamic impedance (the equivalent resistance for small signals when under bias). Bias current, in the above circuit, is nil, so it isn't really
regulating at 4.7V at all.
Accuracy of the voltage at the Zener cathode has two terms: one is the
unit-to-unit variation allowed by the manufacturer, the other is the
current variation (if any) drawn by the Zener times the dynamic impedance of the diode.
For a 4.7V Zener, a 0.5V terminal voltage indicates the bias current
is not sufficient to achieve regulation. 1N4732A is a typical
4.7V Zener diode, and at 53 mA bias (24V source and 360 ohm, 1W resistor)
its equivalent resistance is about 8 ohms.
That makes it a good regulator of its output voltage, since the
fluctuations of the 24V supply only connect through higher (360 ohm)
resistance than the 8 ohm value. It also wastes quite
a lot of electrical power, which is why the 1W rating of the
resistor is important.
That diode can, with air cooling, take up to 1W, so the bias current
could be raised to 200 mA, allowing zero to 150 mA delivered to the load,
while remaining a 'good' regulator. That would mean a pullup resistor
of about 100 ohms, rated for 4W, however.