As someone who works in industrial automation, you're completely going overboard with this.

I can almost guarantee that this goes to a pulse counter. Car drives over, induction coil gets activated and a pulse is output to a counter.

The sheer cost of putting in a PLC to get the high sample rate required to analyse a car is enough to make it extremely unlikely. Not to mention the requirements and costs of the sensor go way way up.

It's just an automated counter, nothing more.

This is just traffic monitoring, it's been around literary for longer than you probably have been alive and its just counting cars, nothing nefarious. It helps with road designs

I imagine that this is for traffic statistics and modeling, and isn't able to distinguish between different models of car

Modern cars and the devices people carry in them emit all kinds of identifying information constantly. There are off the shelf boxes available to collect this information from every car/truck as it passes. No need to get fancy with induction coils if tracking is your goal.

My understanding is the coils are really used for measuring the flow of traffic.

In the US at least, these are generally for monitoring traffic, both current congestion conditions and total traffic over time for planning repairs and changes to traffic pattens. This is the same basic technology that has been used at traffic lights for ages to determine if a car is waiting for the light.

It's highly unlikely they could track an individual vehicle. These can measure the approximate mass of the metal in the vehicle, but not to a specific enough measure that it would be able to determine the difference between similarly sized models of vehicles, much less a specific vehicle. Mostly they just measure to make sure they're detecting a vehicle vs metal trash or something that might be on the road. They are more sophisticated and lower cost to install and power than they used to be which is why they can now be used on moving vehicles vs previous iterations that only really worked for stopped vehicles near existing power infrastructure like a traffic light. But that's about it.

This is not the high tech you think it is.

All this detects is large masses of metal moving over it.
It's used a lot in my area to trigger traffic lights (and annoying if you're on a motorcycle).

It would be too inaccurate to fingerprint a specific vehicle based on the waveform generated as it drives over a coil sensor like this. For example, if your car drives over it one day and then drives over the same coil but 20cm to the left, the waveforms would be different enough already that they couldn't be statistically correlated. A large truck driving over an edge could look like a small car driving directly through the middle. These kinds of sensors are really only useful for saying a big chunk of ferromagnetic something passed by.

Is it possible they are pressure plates for monitoring traffic, with a view to controlling traffic signals etc.

As opposed to the coils (some sort of charging thing for EVs)?

The easier explanation would just be counting vehicles for traffic statistics and management.

Why would anyone use induction coils for tracking when TPMS transponder tracking is cheaper, easier, and less visible?

Even assuming there's a way to uniquely identify vehicles based on their induction signature, digging up roads seems like a literally unbelievable amount of work by comparison.

Unless you're driving a vehicle from the 20th century, the car itself is going to be tracking significantly more information than even the most nefarious possible use of something in the picture.

The gained advantage in your theory lies in drivers being unaware that they're being "scanned." They are not doing a great job at hiding this then, are they. A motorcycle could evade this all together, a car might also be able. And the solar panel could better be used to power a camera and/or a license plate reader if they wanted to know who is passing.

I'm sure if we put enough lab coats on the task they can come up with a system that can ID a model by the reaction in the coil. But at what cost? A light switch is cheap. A light switch that can tell who is using it surely isn't. And why go to this length and not just do the cameras? Ockham's razor.

If I had to guess there is probably a traffic light at the end of that off ramp. They're probably checking traffic patterns to determine the timing of the lights for high traffic times.