I thought I'd look at the Hymns of St Severus and see what he writes about the baptism of our Lord. He wrote quite a few hymns on the Epiphany and they contain various reflections which are relevant to a consideration of 'what was taking place?'.
#15. "..by going down and being baptized in the river Jordan he hallowed the nature of water: and though he is the Son by nature, he receives testimony by the voice of the Father which came from above; and though he is himself the giver of the Spirit, he received the descent of the Holy Spirit. For he that lacketh not, who appeared as one that lacketh and was named the second Adam, became in all things a beginning to us.."
It seems to me that this hymn is stressing that in baptism Christ, the incarnate Word who is the giver of the Spirit, receives his own Spirit so that we might also receive the Spirit. Just as he is baptised, not for any sin, but to prepare the baptismal waters for our baptism.
#16. "..he.. went down into the river Jordan to John, inasmuch as he wished by his baptism to open before us an ascent leading up to heaven, and to lay in advance a sure foundation for the gift of adoption, and to bring the Holy Spirit upon flesh, and to crush the head of the evil one, the supraensual serpent, upon the waters.."
This hymn also uses the idea of the Word experiencing these things for OUR benefit, not his own. He pours the Spirit upon himself so that being united with his humanity we might also receive that same Spirit. He gpes down into the water that he may lead US up to heaven. Everything is for the sake of our salvation and for the will of God. It is not a necessity placed upon him because of his humanity. He is not baptised because he himself is sinful. He does not receive the Holy Spirit because he lacks it. In all cases it is for our sake and our own deficiency not his own.
#17. "..For our sake again, who are guilty persons subject to sin, he is baptized like the rest in the river Jordan like one guilty of sin, not because he needed cleansing, but that he might himself cleanse and hallow the water by his baptism, and illuminate the divine laver, which shone with the rays of the triple and single light of the Trinity through the goodwill of the Father, through the condescension of himself the Son, and through the descent of the Holy Spirit, which he received for our sake, when it flew like adove and came upon hm, though it is in him in essence.."
This again shows that St Severus believe it is for our sake, and not his own, that he is baptised and recieves the Holy Spirit, which he does not lack. This is all by way of a preparation for our own baptisms in which we will share in the life of the Word Incarnate.
#18. "..In proof that it is for our cleansing only and not from need that Jesus, who is God and the Word, our Saviour, is baptized, let us listen to the voice of John... how could he who is able to cleanse the Baptist himself be reckoned among the rest of those that are cleansed?"
Again we see that St Severus does not see that the baptism of Christ is based on any need in himself or in his humanity, but that it is for our sake. Several other of his hymns echo this same point of the baptism of Christ being a hallowing of the waters for our sake, and the beginning of our cleansing.
#22. "..he did not come to receive any addition.."
This reminds us the the Word lacks nothing in Himself or in his humanity.
#24. "..the Son and Word of God who became incarnate and became mam truly without variation from a mother standing in the water to be baptized, and making the water itself a sourec of life, inasmuch as he is himself by nature a fountain of life, and showing the Father, as he crise from above, by saying 'Thou art my beloved Son', bestowing the beginning of adoption on us ourselves and not on Christ for he who is himself alone a Son by nature needed not to become a son; and showing the Holy Spirit flying like a dove and coming from on high, and perfecting for us by his grace the gift of the laver of regeneration. For all things which he has in his essence as God, Christ received himself for us by dispensation, out of his great mercy"
Just as he did not need to become a son, so he did not need to recieve the Holy Spirit, but he was washed in the waters of baptism, given the title of sonship, and received the Holy Spirit entirely for us. In your the terms of Nicholas, it was a demonstration of the Trinitarian economy of our salvation. It was not for any need which Christ experienced as man. It was 'in all things...for us' and not for himself.
Let me also quote from #25 just because it says so much about the true and perfect humanity of Christ in which we believe.
#25. "..The Son and the Word of God, after he had of his own will lived with men as man since he indeed became incarnate and became man without variation, was standing on the bank of the river Jordan as an ordinary man among many; and John also saw him with the eye of the spirit and revealed and pointed him out as with the finger to the multitude...Therefore he that is complete by nature and came for our sake to fulfil all things, he of his own store gave and imparted divine baptism, while he himself received nothing from it, except our salvation, as the only good and merciful one".
We see here that far from receiving anything in baptism, rather Christ, the Word Incarnate, is giving of 'his own store', that is, from his own divine resources and authority. By participating in the Triune act of the Epiphany the Trinity act together to work out our salvation and prepare a means of reconciliation. Christ is revealed, but there has been no change in who he is. He has received nothing new at all.
How can he who is the giver of the Spirit receive it from another? Rather he himself sends his own Spirit upon his own flesh, not that he lacked the Spirit in any sense, but so that it might also be poured out on all those who would be united to his own flesh in their own baptism.