-4 makes sense if you understand that the input -2 is a unary minus operation. So typing -2 then hitting square only squares 2, not (-2). This is the same in eg Python so I'm not sure it's very controversial. I agree it's unexpected, though.

"-4 makes sense if you consider that the calculator is so damn stupid it ignores every convention every single calculator has made in the past hundred years and instead copies behavior of a dumbass language" isn't exactly the praise you think it is.

At no point in the current expression you wrote "-", though. It may make sense that if you type [-] [2] [x^2] [=] then you get -(2²) = -4, but if your current answer is already -2, then tapping x² should result in (ans)^2 = (-2)^2 = 4. Splitting your current answer into a separate unary [-] as in - (2²) makes absolutely no sense.

Most calculators, even CAS ones, simply get this always right. But sadly this is not the first "desktop" calculator that I see getting this completely wrong. And it makes some results outright wrong!

I didn't enter -2, I calculated -2. The x² should have been taking x = (-2).