The Holy Spirit mission to the world is uniquely His own. He acts without any "supervision." He is fully God, does everything according to His own counsel, and does nor answer or report to anyone, including the Father or the Son whom He is equally great as.
At the same time, when the Father was creating the world, the Holy Spirit's mission was already taken into account and fully calculated. The persons of the Trinity held a discussion, as it were, and the entire course of divine providence, from the creation of the heavens and the earth to the return of the last saint into heaven, as ultimately chosen by the Son and utilizing diverse knowledge, was mapped out in complete detail.
A caveat, as before, may be that immediately before creating, the Father knew everything; the Holy Spirit, everything until Judgment Day; and the Son, everything until His incarnation. At present all three persons are fully omniscient.
So, God does not make mistakes.
We can see that the divine persons' glory is equal in magnitude but radically different in kind.