Try connecting headphones (with a series limiting resistor to set a reasonable volume) in place of the "buzzer"? As it's AC coupled, it seems unlikely is it a buzzer with electronics, more likely a miniature speaker.
The upper 100K pot sets a switching threshold balanced against the low DC bias current of the transistor, from the look of it.
The instructions say to set it to 90K to start off with.
The coil on that style is very critical - wind the two identical coils then make the "head" using some rigid plastic so it's all waterproof once finally assembled.
When I built one some decades ago, I started with the coils lightly taped down then started putting blobs of epoxy on as I refined the adjustment, leaving less and less movable for fine tweaking as I went, until it was all solid.
It worked wonderfully for a day or so - but unfortunately I'd made the coil base and lid from hardboard (like 3mm fibreboard) and that absorbed moisture as I used it outdoors and messed it up!
I had varnished it, but apparently that was not adequate weatherproofing.