Live and learn.
Does that voltage drop occur with both carbon zinc and alkaline cells?
Yes, but tends to be worse with zinc carbon, which is one reason why alkaline cells are often used in preference to zinc carbon.
Voltage drop is rather variable, but in general flashlight bulbs are designed for about 1.2 volts per cell.
Some suppliers dont state a voltage but simply give the number of cells intended to be used.
Bulbs for 5 cells are often rated at 5.95 volts, which is almost the same thing as 6 volts, but avoids confusion with 6 volt radio panel bulbs or with bulbs for 6 volt dry batteries which are 4.75 or 4.8 volts.
Large cells or multiple cells in paralel tend to have slightly higher on-load voltages. A paralel pair of 6 volt lantern batteries wil have a slightly higher voltage in use than a single battery. A bulb intended for a single 6 volt lantern battery was typically rated at 4.75 volts, a bulb intended for two such batteries was often 5.4 volts.