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.