reading the white paper, the vertical oscillation cannot be correct, as it will measure it of the foot, but not the body purely itself. A person might lift their foot 10cm.... but the top of their head maybe moved up and down 1cm, where as more inefficient runner also doing 10cm, may have had their head bounce up and down 3cm . So one data point of the foot is not enough... everything is being over approximated

Stryd measures gross external power output. The usefulness of that as a predictor of metabolic cost (or other physiological demands, such as muscle damage as a result of absorbing power) is a different question.

The vertical oscillation that is reported is that of the center of mass, which is calculated from the motion of your foot.

Gross as in financial terms? Sum of all the positive but without subtracting any negative?

Yes, of course. As you well know, net external power when running at a constant speed over level ground is very low.

10K PR: 38:56
Age at time: 42
BMI at time: 18.5
Gender: female

10k PR: 39.43 (Recent PR)
Age: 27
BMI: 21.6
Gender: Male

PR: 39:37
Age: 41
BMI: 24
Gender: Male