Trying to understand what I'm seeing on my oscilloscope
I did a search and seems like the frequency change when a vehicle rolls over those induction loops in the street are quite tiny, as small a small as 0.13% for a motorcycle to several % for a car (% of change in inductance).

That would explain why you can sort of "eyeball" a change in the scope but hard to tell exactly what changed. Excerpt from the Federal Highway page:

"The vehicle classes are:


Class 1: 0.13 percent (DeltaL/L) or 0.12 muH (DeltaL) inductance
change (small motorcycle).
Class 2: 0.32 percent (DeltaL/L) or 0.3
muH (DeltaL) inductance change (large motorcycle).
Class 3: 3.2
percent (DeltaL/L) or 3.0 muH (DeltaL) inductance change (automobile)."


Tons of details on this page:
https://www.fhwa.dot.gov/publications/research/operations/its/06108/02.cfm

So, I'm sure the PIC is used as a frequency counter being driven by probably discrete LC oscillator (Colpitts, you mentioned) with the wire loop as the inductor and sounds like through a transformer. The transformer probably converts the impedance so the number of turns are reasonable to use for a street.

I've used a PIC for frequency counting (monitored a 32 kHz clock frequency down to a few Hz). No ADC is needed, one digital input and one of the PIC's internal timer blocks and some SW code.