To say the three persons of the Godhead are "manifestations" or "essences" is heresy!
In fact, here is a definition:
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Sabellianism: Sabellianism is named for its founder Sabellius (fl. 2nd century). It is sometimes referred to as modalistic monarchianism. The father, son, and holy ghost are three modes, roles, or faces of a single person, God. This, of course, implies that Jesus Christ was purely divine, without humanness, and therefore could not truly have suffered or died."
https://webspace.ship.edu/cgboer/heresies.html
Each of the three are persons (Latin) or in Greek as hypostaseis (pl) or singular: ὑπόστασις. That is:
"(in Trinitarian doctrine) each of the three persons of the Trinity, as contrasted with the unity of the Godhead."
"Mainstream Christian theologians nearly always reject “modalism”, meaning a one-self theory like that of Sabellius (fl. 220), an obscure figure who was thought to teach that the Father, Son, and Holy Spirit are sequential, non-essential modes, something like ways God interacts with his creation. Thus, in one epoch, God exists in the mode of Father, during the first century he exists as Son, and then after Christ’s resurrection and ascension, he exists as Holy Spirit (Leftow 2004, 327; McGrath 2007, 254–5; Pelikan 1971, 179). Sabellian modalism is usually rejected on the grounds that such modes are strictly sequential, or because they are not intrinsic features of God, or because they are intrinsic but not essential features of God. The first aspect of Sabellian modalism conflicts with episodes in the New Testament where the three appear simultaneously, such as the Baptism of Jesus in Matthew 3:16–7. The last two are widely held to be objectionable because it is held that a doctrine of the Trinity should tell us about how God really is, not merely about how God appears, or because a trinitarian doctrine should express (some of) God’s essence. Sabellian and other ancient modalists are sometimes called “monarchians” because they upheld the sole monarchy of the Father, or “patripassians” for their (alleged) acceptance of the view that the Father (and not only the Son) suffered in the life of the man Jesus."
According to Karl Barth:
"As God is in Himself Father from all eternity, He begets Himself as the Son from all eternity. As He is the Son from all eternity, He is begotten of Himself as the Father from all eternity. In this eternal begetting of Himself and being begotten of Himself, He posits Himself a third time as the Holy Spirit, that is, as the love which unites Him in Himself." (Barth 1956, 1)
All of Barth’s capitalized pronouns here refer to one and the same self, the self-revealing God, eternally existing in three ways. Similarly, Rahner says that God:
"…is – at once and necessarily – the unoriginate who mediates himself to himself (Father), the one who is in truth uttered for himself (Son), and the one who is received and accepted in love for himself (Spirit) – and… as a result of this, he [i.e. God] is the one who can freely communicate himself." (Rahner 1997, 101–2)
Similarly, theologian Alastair McGrath writes that:
…when we talk about God as one person, we mean one person in the modern sense of the word [i.e. a self], and when we talk about God as three persons, we mean three persons in the ancient sense of the word[i.e. a persona or role that is played]. (McGrath 1988, 131)
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