It seems that your idea is: sine wave generation-shaping circuit processing-square wave? If so, the intermediate processing circuit should not generate its own signal, but process the input sine wave signal, so it should not be a (square wave) oscillator, but a shaping circuit! If it is an oscillator, who listens to the output frequency? Use LC frequency or your own RC frequency?

It can be shaped by comparator, single threshold comparison and double threshold comparison.

The circuit is slightly changed: C 1 is not grounded, and the collector of Q 1 is connected as the coupling capacitor; R4 is connected to the ground instead of the output, providing a DC path and increasing it to several hundred K to reduce the consumption of the input signal; This becomes a double threshold comparator.

LM324 is a bit slow, so it is better to use high-speed operational amplifiers (TL082, LM3 18, etc. ).