The speed of the pressure wave is one signal that correlates with blood pressure. It's a bit like a string being pulled taut -- waves travel faster with higher pressure. The shape of the wave also gives clues. For example, the rise time of the wave tells you something about the resistance encountered, which is a function of blood pressure.

Rather than hand-engineering these features, most modern systems are built on a wearable foundation model that's been trained reconstruct the signal (similar to how an LLM is trained to predict the next word). Those foundation models are picking up on these signals and likely others.

You're right that calibration with a cuff is required of all systems currently on the market.

The Signal Ring folks' claim they can do a blood pressure number without calibration, which is quite novel and seems to be their "secret sauce". They did run a clinical study as well, so presumably more details will come out whenever that's published.