AKA joule counting- for normal li-ion it gets you to ~5% most of the time, up to 20% off at the start and end. That's assuming the voltage stays constant the entire time- in reality the first bit is at 4.2+ volts, and the last bit is down to ~3 volts. That's a 40% energy difference per electron that leaves the battery.
It's also one of the reasons you get electronics that die suddenly at 5%- current gas gauges usually account for it, but older stuff wasn't always good at knowing when the voltage would drop off. Nowadays (and always, for the most part) the sudden shutoff is because electronics often pull very brief power spikes that drop the battery voltage below the minimum voltage temporarily. The chemistry takes a moment to recover after that.
The problem with Li-S batteries isn't just that they have a goofy curve- that can be charted and saved, even as the battery degrades (Note- I'm mostly up on conventional chemistry. Don't know much about Li-S). It's more have a couple phases they go through during discharge. Impedance and other properties of the battery change, which changes the discharge characteristics of the battery, which changes the voltage. Proportionally, the swing in voltage is also larger (although this kind of thing is always changing, so I may be out of date).
There's also a small amount of self-discharge and parasitic reactions that will consume electrons, but that number is necessarily fairly small and predictable. The main thing is that 50% of the energy variance is in the voltage, and you need to know a lot about the current chemistry inside the battery (as well as the future load profile) to be able to predict the voltage that all the remaining electrons will have as they leave the battery.
Many battery monitoring circuits do this, sampling both voltage and current to compute power over time. With a suitable inductor to limit the rate of current change to be within the nyquist sampling interval of the monitor, you can pretty accurately measure charge going in or coming out of a battery. Combined with a model for the battery and you've got a modern battery monitor circuit.
You could use this technique to estimate the remaining capacity starting from a full charge / known charge, but not to arbitrarily measure the remaining capacity of the battery
It sounds like the voltage curve is all over the place as the battery phases through its chain of different chemical reactions, unlike a normal battery. I take that to mean there's no way to just measure the voltage at a given point of time to estimate capacity, hence why the statistical method was required.
It's a good thing to measure the instant capacity, but the voltage and current (and, hopefully, thermal output) are being measured during the whole flight.
