For one the energy to take a picture is probably enough to power a light for a noticeable amount of time.
And if it isn't, a capacitor that absorbs energy and only allows energy through once it's full would allow the light to remain on for a couple of seconds after power subsides.
About being slow, I suppose it does run windows and its infamous 'defender'
I thought this was a solved problem, like, decades ago? At least I remember even the first gen MacBooks having accurate battery percentages, and it’s a more vague memory but my PowerBook G4 did too I think.
Same for your Windows idea...
To put it simply: the charge level, usually, is just a lookup table for voltage (not under load).
I do not know whether the battery is actually experiencing that sudden loss in charge, nor do I care, because in practice the end result is the same...