Why can an airplane stall in a steep level turn even if its speed seems safely above the usual straight-flight stall speed?

Answer: The wing's angle of attack becomes too high

The turn lowers the airspeed below the stall speed — Speed can fall during a sloppy turn, but that is not the point of this question: it says the speed still looks safely above the straight-flight stall speed. A steep level turn raises the lift demand and pushes the wing toward a higher angle of attack. That is why the stall boundary can move even before the airspeed looks alarming.

The engine stalls as the bank angle increases — No. An airplane's wing stall is not the same as an engine stalling, even though the shared word makes the mistake easy. The engine can still be producing power while the wing is meeting the air too steeply to make smooth lift. Training even includes power-on stalls to show that power does not cancel the wing's angle problem.

The wing's angle of attack becomes too high ✓ — Right. A stall happens when the wing meets the oncoming air at too steep an angle, not when a magic airspeed number is crossed. In a level turn, the wing must make extra lift to support the airplane and turn it, which pushes the pilot toward that steep angle. The FAA example is vivid: a 60-degree level bank raises stall speed by about 41 percent.