simplifying expressions – Is this behavior of the Series function correct

While series expanding a function, I got an unexpected result, which seems like an error to me. I have boiled it down to this minimum (non) working example:

$Assumptions = p (Element) Reals && x (Element) Reals;
k = Conjugate((x^2*(1 + I *p))^2 - x^2*(1 + I*p));
Expand(FullSimplify(Series(k, {x, 0, 2})))
Series(FullSimplify(k), {x, 0, 2}) // TraditionalForm

This returns

-x^2 + I p x^2 + x^4 - 2 I p x^4 - p^2 x^4

and

I (p+I) x^2+O(x^3)

The second output, where I have first used FullSimplify returns the correct output. To my understanding, the first output is wrong. Have I found a bug, or is there something about the Series function I don’t understand.