>>Does this mean Mary is the mother of the Holy Spirit as well??<<<
No. She is the Mother of Jesus. Is Jesus not God?
True, and by which logic Mary's parents were grandparents of God, and believers are brothers of God, and the Jews and Romans killed God. But which is misleading and inconsistent with Scripture. For one, the normal unqualified conveyance of this is that if ontological oneness, while Christ is the Creator of Mary and she contributed nothing to His Deity.
And the Holy Spirit is careful to make that distinction when stating the Christ came out of Israel: "of whom as concerning the flesh Christ came, who is over all, God blessed for ever. Amen. (Romans 9:4-5) And nowhere calls Mary the Mother of God, nor believers "brothers of God," which also sends a confusing message and risks blasphemy.
Such is not the language of the Spirit, who is very careful about giving titles, and refrains from giving glorious titles to mortals, while Mother of God is part of the egregious unScriptural exaltation of one whom the Spirit says little of, and what is said is not even close to the Catholic extravagance, which thinks of mortals way above what is written, contra 1Co. 4:6.
The objection of Ratzinger to Co-redemptrix as contrary to language of Scripture at least, is also applicable to Mother of God though he dare not go that far.
, when asked in an interview in 2000 whether the Church would go along with the desire to solemnly define Mary as Co-redemptrix, then-Cardinal Ratzinger responded that “the response of the Congregation for the Doctrine of the Faith, is, broadly, that what is signified by this is already better expressed in other titles of Mary, while the formula “Co-redemptrix†departs to too great an extent from the language of Scripture and of the Fathers and therefore gives rise to misunderstandings†(53).
He went on to say that, “Everything comes from Him [Christ], as the Letter to the Ephesians and the Letter to the Colossians, in particular, tell us; Mary, too, is everything she is through Him. The word “Co-redemptrix†would obscure this origin. A correct intention being expressed in the wrong way. “For matters of faith, continuity of terminology with the language of Scripture and that of the Fathers is itself an essential element; it is improper simply to manipulate language†(God and the world: believing and living in our time, by Pope Benedict XVI, Peter Seewald, Ignatius Press, San Francisco, 2000, p. 306