"As I understand the task, the amplifier should work in the quasi-linear range with a gain of 100.
Hence, the transistor is neither turned (switched) ON nor OFF."
To start with, you are missing the whole point of my discussion.
The output transistor will be fully turned ON. The base bias resistors are trying to put 2v on the base and this is more than enough to turn the transistor ON.
The 10k will deliver about 1mA and if the gain of the transistor is 100, this will produce 100mA through the 220R load resistor. The voltage across the resistor will be 220 x 0.1 = 22v which is clearly more than the supply, so the output transistor will be FULLY TURNED ON.
As far as the output stage turning OFF, you will have to do some more involved calculations to determine if the 1u will turn the stage OFF.
This is not important because you can see the amplifier is so badly designed that it is not worth implementing.
As I said before, you have to look at a circuit and "see"what is happening in a general sense and do the accurate calculations after.