Essential Supremum and Supremum in anticipation

Suppose that $${Z_i } _ {i in I}$$ are a family of densities in $$L ^ 2 ( Omega, mathcal {F}, mathbb {P})$$, and $$X = L ^ 2 ( Omega, mathcal {F}, mathbb {P})$$, When is it true?
$$sup_ {i in I} mathbb {E} left[Z_icdot (X- mathbb{E}[Z_icdot X|mathcal{G}]) ^ 2 Law]= sup_ {i in I} mathbb {E} left[Z_icdot (X- operatorname{esssup}_{i in I}mathbb{E}[Z_icdot X|mathcal{G}]) ^ 2 Law]?$$

I've seen similar questions, but I have not encountered anything like that here.