Voltage gain at 10kHz of the three stages is about 1,200 which is lots of gain, very sensitive. Layout would matter. Anything I've built like this oscillates.
I'm guessing it's an electrostatic probe, with the LED showing detected RF. These are very useful sometimes, pays for itself in saved time.
For many decades, I've used the crapola
LM386 Av=200 in a (contact probe) signal tracer with loudspeaker, or headphones if I need to track interference or listen for ghosts. The LM386 is a true piece of shit, high distortion, loves detecting AM radio, prefers to oscillate, so finding a malfunctioning stage is difficult with it. But it does the job and I'm too lazy to build something better.
I did an LT Spice sim on the Super Probe and it kinda confirmed what I was thinking.
Common emitter stages with no local feedback do have high distortion and are finicky about transistor hFE for clipping.
2N3904 beta=300, collector is at 0.25V
BC547 beta=458, collector is at 0.15V
BC847 beta=182, collector is at 1.4V
But the input stage has a low input impedance, it loses a lot of signal when you have high Z capacitive-coupling from the probe. I'm saying the probe loses much "in the air". A JFET would be ideal there and then you need less circuit gain to make up for air losses.
I would use that and add some DC feedback for biasing the BJT's.
An SMT version, would be nice to stuff the probe in a pen with foil shield inside.