Analysis of BJT RC Phase Shift Oscillator
Please guide me where I am wrong because I am a beginner in
electronics.

You have miscalculated the parallel impedance of the RC network and the 10 kΩ collector resistor (R4). It's more like 9540 Ω than 8 kΩ. The mistake you have made is that you have assumed the impedances are just paralleled like parallel resistors but this isn't the case when the first 10 nF capacitor is dominant.
So, if you assumed that the 10 nF was directly loading the 10 k&amp;ohm R4 resistor, the parallel impedance would be this produced by this calculator: -

So now, the gain will be dominated by that impedance and the 1 uF capacitor in the emitter. That yields a gain value of 30 i.e. suitable for oscillation.
But, of course, the 10 kΩ resistor isn't directly loaded by a 10 nF capacitor (worst case) and so, the net collector impedance will be a little higher and there will be more gain.