Small-signal analysis of transformer BJT oscillator
The redrawn oscillator does not work. The polarity of one of the coils is reversed compared to the original. The operation of the oscillator is significantly affected by the capacitance of the secondary winding with a large number of turns. The diode load does not change the essence, it would only greatly prolong the simulation time. Charging the large capacitor to 300V is a long time. The circuit is strongly nonlinear, the linear model cannot be used here. The transformer is the standard flyback, with approx. 10uH  primary inductance. This determines the (no load) frequency of the oscillator.