They were unprotected batteries, and when I put them in my PicoCalc recently, I may have put them with reverse polarity, which caused them to vent. I instantly removed the batteries from the PicoCalc, and I don’t think any damage has happened to my PicoCalc’s battery holder.
18650s aren’t simply “better AAs”. You need to treat them with respect, and don’t just assume that everything will be ok if you do something dumb. Any time you have a loose cell you have to think through everything you’re doing before you do it, then stop and check again.
And “protected” cells aren’t magically safe either - they can potentially prevent certain classes of failure, but they’re not idiot proof, and they can make you complacent.
The picocalc is a single cell device - or more accurately, it’s a 1s device. If you put two cells in, they’re connected in parallel and are electrically identical to a single cell with twice the capacity. The AXP2101 is being used appropriately.
That actually brings up another issue with using 18650’s here - if you put two cells in, they must be charged to the same level (within 0.1v!). Otherwise the higher voltage cell will pump current into the lower voltage cell uncontrollably. This is bad. The simplest way to deal with that is just to fully charge each cell independently with the same charger before installing them. Once they’re installed and at the same level, they’ll remain matched.
Also, as my batteries short circuited, and so did my Pico 2W, the sd card slot, keyboard stuff, display, and some key circuits are guaranteed not to be short circuited, but about the battery holder, and the pin slots to hold the Pico, I don’t know about them. Because, this buzzing, may be caused by the short circuiting, or the high amount of power, been given through mains, as appose to the power you would get with batteries.
From other early posts, I believe you swapped out the original Pico, with a Pico2, so I’d try swapping it back in to see if it still makes the noise. If the noise goes away, it means the problem is with the Pico2 and not the PicoCalc itself. If that’s the case, I’d wipe the Pico2 and reflash it to see if that makes sny difference.
Off hand, if the PicoCalc is otherwise working, the only other things I can think of that could possible make a buzzing sound is the audio circuitry or the backlight… We ran into noise from backlights occasionally in my old company.