Some additional comments:
One needs to differentiate between a regular regenerative detector/receiver, and a superregenerative ditto. Their schematic may at first blush look eerily similar, yet their method of operation is completely different.
A classic regenerative RX generates a continuous sinewave oscillation at or very near the intended receiving frequency. The RF input signal from the antenna is mixed with the LO signal and an audio or supersonic low frequency signal is the result. This is where the frequently seen audio transformer comes into play in your MW broadcast regenerative RX. So with a regenerative detector you'd expect to see a single frequency being radiated by the detector.
A superregenerative detector is a completely different beast. In this the oscillator is continuously driven into and out of oscillation, usually at a supersonic rate, called the quench rate. Thus the name. The trick is that when the oscillator is turned on, the gain of the RF transistor is 'slowly' increased up until the onset of oscillation. This is done by using some form of positive ramp on the base current.
When an oscillator starts up, it is the noise in the circuit, which provides the initial 'seed' for the amplifier in the circuit. This is the effect, which is (ab)used in a superregenerative detector. How this works is, that at the point of onset of oscillation, the time it takes for the oscillations to exponentially ramp up from the local noise level hugely depends on whether - by coincidence or design - a (very) low level signal is injected into the oscillator from the outside. This effect is ridiculously sensitive, so a supersonic detector is quite a bit more sensitive than your regular regenerative detector with continuous oscillations.
The oscillator thus converts RF input level from the antenna/ambient into time it spends at full oscillation amplitude. Higher signal level means it ramps up much quicker. IE. the DC power input to the oscillator, averaged over many quench cycles, indicates the ambient RF level around the RX frequency. If, like in this case, the quench rate is several hundred kHz, then you can easily detect data bit rates from the transmitter of several thousands. Just measure the voltage drop across a fixed resistor, or, like what is maybe used here, use a simple diode detector of the RF oscillator signal.
So the oscillator ramp up waveform depends heavily on the ambient RF noise/signal level. Which means the ambient RF noise around the RX frequency modulates the oscillator, which in turn is the main reason for the ridiculously wide noise piedestal you see on the SA.