In 1981 I got a Casio hand calculator: LCD display, running on one AA battery. I never turned the power switch off. I used it daily for a decade and after 25 years found it, and it was still functioning. Under a quarter century of grime. I recall over 30 years ago when the first chip was released for flashing an LED with a very short duty cycle. It was postulated that the batteries (way before Lithium-ion and when NiCad was the Gold Standard) would last longer with a very slight current drain. It seems they were right.
Not sure about longest lasting battery but it always makes me smile when I see a single AA battery quartz clock on a wall struggling to overcome gravity with the big hand stuck at about 20 minutes to the hour still ticking away.
When a quartz clock can no longer keep the arms moving its time to finally retire the battery.
When I have a remote control or other device with an (allegedly) dead battery, I save it for use in the wall clock. I can usually get another couple months of power using the battery in the clock before it finally 'gives up the ghost'
Across the hall from me, my colleague has an hp-15C calculator that he has had since college 25+ years ago that is still going on the original button batteries. He does only use it a few times a month on average, but still, that is a long time.
Separate application, but my father bought a Sony transistor radio in the 1960s... one of the earliest. We still have it. It still works like a charm. We listened to some historic events on that thing...
I have a HP-15C calculator and a HP-12C. I haven't used them much in the last 7 years but when I pulled them out they still work. I didn't buy either one new so I can't tell you how old the batteries are except they are both more than 7 years. Some SOB stole my HP-15C about 12 years ago so I had to buy one on eBay. Why would an EE use any other calculator?
I'm afraid to leave common, alkaline batteries in anything nowadays for very long without regularly checking them. I have had so many things destroyed when they leak and/or grow the white chemical "fuzz". It's really frustrating. Do modern-day batteries do this more than they used to?
I won a sales contest and was awarded a "high tech" Sharp Elsi Mate EL-24 portable calculator back in 1977. Everyone was wowed by this, at the time, as some high schools still used slide rules. Going through an old drawer earlier today I ran across this amazing device and found that it is still workin on the original batteries!