According to Trinitarians, why does Jesus glorifying himself amount to nothing? John 8:54-55 has Jesus saying

&quot;“If I glorify myself, my glory is nothing. It is my Father who
glorifies me, he of whom you say, ‘He is our God,’ though you do not
know him. But I know him; if I would say that I do not know him, I
would be a liar like you. But I do know him and I keep his word.&quot;

For unitarians, this makes sense - Jesus is a man, the Father is God, and so what is important about Jesus is that the Father (= God) glorifies Jesus, not that Jesus might glorify himself.
For Trinitarians, why would Jesus, who is God, glorifying himself be 'nothing'?
There is a lack of appreciation for the fine and complex texture depicted of the existential and operational relationships among the three of the Divine Trinity in the activities of the incarnated Son.
Especially in John, there is an almost maddening interplay between the operations of the Son of God and those of the Father and the Spirit.
We are not observing the life of simply a man nor of God become a man in the simple sense of who God is; instead, we are seeing the entire Triune God in operation in the actions of the human life of the incarnated Son of God.
As Jesus is about to die and resurrect for our redemption and justification, the Son asks the Father to glorify Him withthat eternal glory once set aside, and in doing so, to glorify Himself along with the Son.
In so saying, the Son enunciates a principle within the Trinity, that is, that the Son is glorified in the glorification of the Father and the Father is glorified in the glorification of the Son. So in this case, God and man are joined together as one entity, living and working together as one. So, if the Son in His humanity glorify himself, it is nothing and meaningless because all He express is just Himself.
The prime function of the Son’s incarnation was to glorify the Father on earth, and the Son fulfilled this mission by finishing the work the Father had given Him to do (John 17:4). This mutual glorification can hardly be viewed as two separate actions of the Father and the Son, but as one action in which the Father and the Son both act; however, the agency of each has a distinct object —the other— and the agency of each requires the operation of the other. So blended are the actions and operations of the Father and the Son in this mutual glorification that in one breath the Son can speak of Himself being glorified and in the next of the Father being glorified (John 12:23, 28).
Torrance puts this clearly:

It was, of course, not the Godhead or the Being of God as such who
became incarnate, but the Son of God, not the Father or the Spirit,
who came among us, certainly from the Being of the Father and as
completely homoousios with him, yet because in him the fullness of the
Godhead dwells, the whole undivided Trinity must be recognised as
participating in the incarnate Life and Work of Christ. - Thomas F.
Torrance, The Christian Doctrine of God: One Being Three Persons
(London: T&amp;T Clark, 1996), p. 108
Since God’s Being and Activity completely interpenetrate each other,
we must think of his Being and his Activity not separately but as one
Being-in-Activity and one Activity-in- Being. In other words, the
Father, the Son and the Holy Spirit always act together in every
divine operation whether in creation or redemption, yet in such a way
that the distinctive activities of the Father, the Son and the Holy
Spirit, are always maintained, in accordance with the propriety and
otherness of their Persons as the Father, the Son and the Holy Spirit.
This may be called the ‘perichoretic coactivity of the Holy Trinity’…
The primary distinction was made there, of course, for it was the Son
or Word of God who became incarnate, was born of the Virgin Mary, was
crucified under Pontius Pilate, and rose again from the grave, and not
the Father or the Holy Spirit, although the whole life and activity of
Jesus from his birth to his death and resurrection did not take place
apart from the presence and coactivity of the Father and the Spirit.

Ibid., pp. 197-198


Some other quotes that helps to describe this reality:

Perichoresis means that not only do the three members of the Trinity
interpenetrate one another, but all three are involved in all the
works of God. While certain works are primarily or more centrally the
doing of one of these rather than the others, all participate to some
degree in what is done. Thus, while redemption is obviously the work
of the incarnate Son, the Father and the Spirit are also involved. -
Millard J. Erickson, God in Three Persons: A Contemporary
Interpretation of the Trinity (Grand Rapids, MI: Baker Books, 1995),
p. 235


When Scripture ascribes certain works specifically to the Father,
others specifically to the Son, and still others specifically to the
Holy Spirit, we are compelled to presuppose a genuine distinction
within the Godhead back of that ascription. On the other hand, the
work ascribed to any of the persons is the work of one absolute
person. - Cornelius Van Til, An Introduction to Systematic Theology
(Philadelphia, PA: Westminster Theological Seminary, 1961), p. 228


When believers complain that they cannot distinguish between the
separate activities in their lives of the Father, the Risen Lord, and
the Holy Spirit, the matter is sometimes phrased in a way that
obscures God’s unity, a fundamental doctrine of both the Old and New
Testament. Every action of any of the persons of the Trinity is an
action of God, although in many actions the persons of the Godhead may
be active in different ways. All authentic spiritual experience is an
experience of the one God. - Carl F. H. Henry, God, Revelation and
Authority, VI:2 (Waco, TX: Word Books, 1983), p. 400