Usually you estimate the charge left in a battery by checking the voltage. An ideal voltmeter has infinite resistance. An affordable mechnical voltmeter might have 100,000 ohms of resistance while testing a battery. Simple electronic voltmeters (like the vacuum tube voltmeters they had in my high school physics lab) get into the millions, precision test gear today has billions of ohms of resistance.
Now it takes a little power to power the voltmeter, but not a lot. A cheap DVM isn't much more complex than a 1970s digital watch. A smoke detector has a low battery detector that is good for years.
If you just want to know if a alkaline AA battery is good or not, checking the voltage is good enough.
When the battery is under load, the amount of voltage drops, and when the load is released you often see the battery voltage recover gradually over the course of a minute or so. A good discharge controller would be built with that phenomenon in mind.