why does the Why does the activation energy of a reaction not appear in the final $G$ of the reaction?

The final $G$ of a reaction depends only on the rates of the forward and reverse reactions.

The activation energy is released when the transition state proceeds to product.

The final $G$ of a reaction depends only on the free energy of the substrate and the transition state.

Enzymes reduce the activation energy to zero by promoting the formation of the transition state.