[otter-rock]

You cover a lot of interesting topics. Some exposition:

Reporting power is easy with the power triangle. It's a mathematically exact concept.

Measuring power is a different story. Distortions of the assumed perfect sine wave create measurement errors. Meter bandwidth matters, but most have low bandwidth.

Grid meters at least use voltage phase, if not magnitude. Residential customers are billed only for real power, so the phase information is necessary to exclude the reactive power from the measurement.

One rating is for maximum output. The other describes a short-circuit that you can create with an overly reactive load.

The degrees of freedom complicate the implementation, but the bottom-line discussion abstracts away those details.