OK, lets outsource the voltage curve integration to HKJ. Samsung 35E . IIRC 7135 loses at least 0.1V even when Vf is below battery voltage.
For Vf = 2.8V we don’t need to be concerned about what happens below that voltage because that’s already the cutoff. We need 1A but we can use the data for 2A to account for resistance outside the driver (that’s arbitrary). We got 11.838Wh/3.327Ah = 3.558V avg. under load, but it can be done without using that voltage, we have 3.327 * 2.8 = 9.315Wh out. 9.315 out / 11.838 in = 78.7% efficiency or 21.3% loss. 2.8V / 3.558V gets the same number. I know I’m neglecting significant figures.
For Vf = 2.9V, lets assume that we lose a constant value of 0.1V in the unregulated region, we have 3.2Ah above 3.0V and 0.127Ah below. The regulated region contains about 11.5Wh, 11.5/3.2 = 3.59V. So we lose (((3.59 - 2.9) / 3.59) * 3.2 + 0.1 * 0.127) / 3.327 = 18.8% loss (with many sources of errors).
For Vf = 3.3V I think the regulated region ends at 3.4V, have 2.35A, 8.5Wh above = 3.62V avg, 0.977Ah below, so (((3.62 - 3.3) / 3.62) * 2.35Ah + 0.1 * 0.977Ah) / 3.327 = 9.2%. I took the wrong data as the current is about 3A rather than 1-2A but that correcting that will only increase the efficiency.
The point is that linear drivers are quite efficient when the Vf is about 3.3V or higher, for example when running a SST40 at 4.5A, but they lose efficiency at low current where the Vf is lower (overall driver+led efficiency still increases).
That’s the first chart with many colors, 2 lines for each load as there are 2 samples.