> Bias is different from precision. If both conditions have the same bias, their difference is still unbiased.

Not really, and I wouldn’t assume that when the condition under study can also affect how the measurement is taken.

> If you quantize so much that you have no variance in the measurements, then sure. But watches typically have 1 bpm quantization, which is fine at the scale of variation in HR.

At the scale of variation in HR in general yes, but not if the difference you’re trying to measure is in the range of 3 BPM.

> If you have independent error in measurements and quantization that gives you variance in measurement

That’s a big if. I am not confident we can claim that the errors are independent in this case, using sauna or not can affect how the sensor measures BPM.