I tend to just short non-rechargeable AAs on the 10A/20A DMM range and see what the amps is (Only a quick tap, like for 250ms).
If i see above 3A then I consider it ok. If it's below 1A it goes in the trash.
I find this tells you more than voltage. It's more of an ESR test. But some people don't like shorting them like that.
Shorting a rechargeable AA will easy push 10A so probably not a good idea, and a non-rechargeable lithium alkaline is probably not a good idea either if your DMM fuses are expensive

I've never blown a 10A DMM fuse doing this but YMMV.
I usually do a voltage test first when I think it could be a fresh cell (1.5V etc) But if it's <=1.3V I do the 10A scale shorting test to see what it's current sourcing ability is. If I know it's not a fresh cell then i go straight to the short test.
I would never do a short test like that with LiPo/LIon/NiCa cell. NiMh is borderline
If i wanted to check current sourcing on those i would insert a load resistor