Why is no PWM signal generated using Timer 2?
The output compare unit of timer 2 is connected to pins PB3 (OC2A) and PD3 (OC2B). So you have to configure those as outputs.
Keep in mind that you can't choose any pin when using hardware pwm, this hardware feature is linked to specific pins.

You also have to set COM2A1 in TCCR2A. Otherwise OC2A is disconnected from the output compare unit (ref: Table 17-3 in datasheet).
The effect of COM2A0/1 depends on the configuration in WGM20-WGM22.
The same applies to OC2B respectively.