10 years ago most of these battery packs were relative to the 5V output voltage, so they advertised lower amp-hours. That stopped making sense with fast charging at higher voltages so they restandardized on 3.7V.

But watt-hours would make infinitely more sense for all batteries.

Huh, I didn't get that memo so have been played a fool assuming 5v until now. Advertising mAh corresponding to a different unadvertised voltage than the output is just misleading advertising.

Then the fact we’ve “standardized” on mah as the unit is just another in our long proud tradition, same reason we still use “Watts” as the main measure of light output, even when it has to be made up for use on LED bulbs.

Could as least use Coulomb (or just count electrons), instead of taking Current = Charge / Time and multiplying by charge again.

For what it's worth: 1 mAh ~ 2.25 * 10^19 electrons. Or with SI-prefixes: 22.5 exa-electrons (= 2.25 Ee).

Mostly all flashlights advertise in lumen though? I suppose you mean light bulbs?

Yes, I mean the bulbs. Generally in the US at least we find them in the store labeled like "40 watt equivalent (small print: 2.1W)"

Not necessarily, no. If you have multiple batteries in series for a higher voltage pack, then it'll be less for the same amount of energy stored. But then the marketing for these packs will happily abuse the units to get the biggest numbers.

Internal voltage is chemistry dependent. In other words, cell manufacturer invariant. It's 3.7V for NMC, 3.2 for LFP, 2.3 for LTO, 3.0 for Na-ion.

Technically speaking, the pack voltage as well as Ah rating should be that of the pack and not cumulative total of the pack; two NMC 18650 in series should be 7.4V 2600mAh, not 3.7V 5200mAh. But denoting as if all cells are in parallel allow this figure to be maximally inflated and so that's what manufacturers do.

High voltage charging etc are not relevant. Though, high voltage assembled battery packs should be marked in that high voltage amp-hour ratings.

The technical reason why amp-hour rating exist is because there are parameters dependent on amperage than energy or voltage, such as thickness of the wire to be used in the device or cycle life of the cell. Voltage of a battery also kind of change proportionate to remaining energy in it, and values like 3.7 for NMC or 1.5 for Alkaline is a 50%, averaged, state.