The incarnation is beyond reason to understand other than God being almighty, I believe the hypostasis union of the Word made flesh explains the incarnation fairly well.
But we can understand the basic principle of the one true God the Father almighty.
I will say that God is now in a new life and that new life is a true human life.
The Son(Word) when made flesh Was given a true human life in his hypostasis and this human life is genuine and true Jesus is all of who and what God is in and as a true man.
The reason that this would not be Arianism is because the Son has a real existence before the incarnation in eternity as the Word of the Almighty God.
And the reason also as to why it is not a different God is because Jesus is God himself expressing the fullness of his nature as a true man therefore this real man can pray and do all things as a real man and not be affected in his eternal deity.
All authority of the Father is given to the Son so that the Son has authority as the Father in his humanity because the Son of God is the exact character of God imprinted in a human ousia and of one hypostasis of the Word.
The reason this would also not be Nestorian is because there is one type of hypostatsis of the Son of God, But that there are two ousia of the one hypostasis of the Word, So it is not a different God who was made flesh but the one God was made flesh through His Word becoming man.
If it were Nestorian then Jesus would have two hypostasis and two ousia.
But we know that the Son of God is one existence”hypostasis” both God and man fully God and fully man, the reason the Son of God does the works of the Father and will of the Father is because it is the one divine will of the Father, the one divine work of the Father, and the one authoritative power of the Father.
So you have one divine consciousness that is eternal and one true human consciousness that is now united with the divine in one existence as the Word of God Jesus Christ.
To put simply, God would be Jesus if God were a man and he is, Jesus would be God if he were God and he is.
@OddBird modalism is not Sabellian, the modes Sabellius speaks of is that there is one hypostasis of the Father and that the Father’s existence was made flesh, so the Father was therefore born, the Father prayed to Himself, and the Father was crucified.
Mode in Sabellianism is merely a way in which one expresses his existence. Modalistic Monarchianism or anti social trinitarianism teaches that God subsists or exists in three hypostasis, underlying realities.
Meaning, the Father who has a real hypostasis is the one ousia(substance) and necessitates the other two hypostasis or real existence of the Word(Son) eternally begotten and the Spirit which is proceeding from the Father.
Each are not a different ousia of the Father but are of the same ousia, homoousia, the Son is a distinct hypostasis or mode of existence, a real subsistence who is of the same ousia of the Father.
To put plainly, since the Father is therefore the Son is and therefore is the Spirit also.