That's probably a hardware issue. Old batteries start to drop voltage under high load or on low charge %. This causes the phone to glitch or just hard reboot if the voltage drops below spec. Likely just have to get a battery replacement.
I think it is probably only a hardware issue in the sense that the iPhone 13 mini is probably too old/slow to run iOS 26 as quickly as the old version.
I updated my old/spare phone - an iPhone SE3, which I think has a similar processor and memory (A15 and 4GB). It became a lot more sluggish. I learned my lesson not to upgrade my main phone, also an iPhone 13 mini.
I also noticed a disappointing slow down on a 9th gen iPad, which has even older internals. Actually, perhaps I should be quickly looking into downgrading that if it's possible.
I updated a 13 mini and it stared off really, really slow for about a day, when background processing happens I assume. But then it got to similar speed as before, however jankier, as usual with iOS 26. That being said, it’s a unit with over 80% battery health. Otherwise the CPU gets throttled.
iPad Pro 3rd gen definitely got much more sluggish with 26. Wish I hadn't updated it now, but wanted to try the new windowing paradigm (not really worth it on a 12" screen).
