I learned negative as being a separate operation where we need to apply the order of operations. I think it was something like : -2 is a diminutive for -1x2 so it uses the order of operations of a multiplication.
My calculator is the official one used in schools in France (ti-83 premium ce) and it says -2^2 = 4 with the negative key. I don’t think it would make a mistake in such a simple concept.

But whatever these concepts can change depending on the field, country, level of education. What I mean is : it’s unclear, so use parentheses. So (-2)^2 or -(2^2) are the correct ways to write it.