Buy rechargeable. The rechargeable batteries sold at Lidl and IKEA are excellent in my experience and quickly pay for themselves. Just start cycling single-use batteries out as they expire and it’s easier to keep track of who you’re supporting with your purchase when it’s a single annual purchase rather than something you buy every time you’re at the supermarket.

I saw a Project Farm video where they tested various AA batteries, alkaline and lithium.

One of the tests was how long each battery could run a fan with a constant energy draw and Varta Longlife got the worst score by far.

Those had a made in Indonesia label though, I don’t know if they have different plants in Germany with better specs under the same name.