I expect it is finding a way to measure multiple frequencies around the tuned station and decodes the data from it’s deviation from the tuned frequency?

Yep, and that’s bandwidth. Up to 200kHz for WFM I think.

Edit: I’ll add some images. Maybe they could be helpful.

---

This is screenshot of RF spectrum. Frequency increases to the right, time towards bottom. On the left is some regular FM station, on the right is signal from my cheap FM transmitter. It’s mono-only making it perfect for this test.
The white rectangles show filter bandwidth and red line center frequency. That’s what you tune, center frequency.

In this image it’s just transmitting unmodulated carrier wave. In other words, silence.

Here I modulated it with a simple sine wave. I slowly increased its frequency over time. Probably seems familiar. (It looks like dots because the spectrogram is drawn at 20FPS. With high enough framerate it would be a continuous line.) Frequency dictates how often the carrier wave swings.

Here we’re back to 1Hz sine wave, but instead of changing the frequency, I changed its amplitude (volume) up. The further the frequency deviates, the higher the amplitude. (Again, 20FPS. It’s not changing the frequency suddenly like that.)

For the sake of making it a continuous line as it is, here it’s shown at 600FPS.

You can see the FM station at the left starts to fall apart into waveform a bit as well.

Of course, music, speech or whatever isn’t a single sine wave, it’s a sum of range of frequencies of different amplitudes so it doesn’t look that nice.

Of course, don’t trust me on anything. I likely said something wrong.