According to Trinitarians, which person/essence/being/substance/relation is "the Living God"?

The Living God is the One who we receive in the Eucharist

I received the living God, and my heart is full of joy.

https://hymnary.org/text/jesus_said_i_am_the_bread_kneaded_long

Now, I would like to see a question "Is the the Eucharist the Body,Blood,Soul and Divinity of Jesus or the Trinity"

And another question "How can Jesus be the Priest and the Offering?"

this is

A great mystery, a mystery of love, an ineffable mystery, before which words must give way to the silence of wonder and worship. A divine mystery that challenges and involves us, because a share in the Trinitarian life was given to us through grace, through the redemptive Incarnation of the Word and the gift of the Holy Spirit: "Anyone who loves me will be true to my word, and my Father will love him; we will come to him and make our dwelling-place with him"

https://www.vatican.va/content/john-paul-ii/en/audiences/1999/documents/hf_jp-ii_aud_10031999.html

but the Trinitarian understanding of God far exceeds the Unitarian one because it keeps the mystery, it lets God operate on His own terms so we can become partakers of His nature, not attempt to be His Master through our own knowledge.

The three divine Persons are present in the sacrifice of the altar. By the will of the Father, with the cooperation of the Holy Spirit, the Son offers himself in a redemptive sacrifice. We learn how to personalise our relationship with the most Blessed Trinity, one God in three Persons: three divine Persons in the unity of God’s substance, in the unity of his love and of his sanctifying action.

https://opusdei.org/en/article/the-eucharist-and-the-mystery-of-the-trinity/

Being a Christian and getting to know God is so much like marriage, it's not surprising that the Bible mentions it over and over again. In marriage we try to get to know one person who is like us but entirely different; who we're cut from the same image of. But in Christianity, we get to know Three Persons who made is in Their Image and our brains turn to mush at the very though of it.

As the one living God cannot be divided into parts, then it is the Father and the Son and the Holy Spirit sharing the one, divine nature in the absolute unity of the Spirit who subsist in this one living God. This touches on the person of God.

In a chapter entitled "The Living God", this is made clear. The trinitarian author deals with the "Simplicity" of God, in brackets, (Unity). I quote:

"'Simple' means undivided and indivisible; not complex or made up of different things. For example, a jacket made entirely out of wool is simple in its fabric, while one composed of different fabrics is complex. To say that God is simple is to say, first of all, that he is pure spirit. We are made up of different parts. Not only are we composed of spiritual and physical aspects, even our soul and body are complex. The soul has capacities for thinking, desiring, and willing, and the body is composed of a host of different parts. However, God is not composed of different faculties or parts.

One of the important implications of divine simplicity is that God's attributes are not literally different aspects of God's essence but various descriptions of God's unified being...

We live, but only God is life and possesses life "in himself." In fact, this is the point Jesus made in John 5:26, claiming this divine attribute for himself as well as the Father." Pilgrim Theology pp. 74-77, Michael Horton, Zondervan 2011

I stop the quote after just that one example of how God having life in himself is also true of Christ. That is one way of showing how we cannot separate the living God from Christ. The book has a great deal more to say on this, and other aspects of how God cannot be divided into parts, nor should he ever be viewed that way. This touches on the essence and being of God.

That is why, when Peter had revealed to him by the Father, through the Holy Spirit, that Jesus is "the Christ, the Son of the living God", Christ rejoiced at this turning point in Peter's understanding. It has to be revealed. It is not about verbally assenting to a formula of words regarding God; it is about entering into personal, spiritual relationship with God through proper, heart-felt confession of Christ as "the Christ, the Son of the living God". The Holy Spirit's role is to convict repentant people, to lift Christ up, and so all three are involved in bringing spiritual life to formerly spiritually dead people. Once that has happened, the reality of the living God begins to grow. This touches further on the person of God, and relating to him. But if this never happens, the whole idea of the triune God will just seems peculiar, if not downright ridiculous.

That is why the start of entering into this spiritual relationship with God will be, as the Psalmist declared, "My heart and my flesh cry out for the living God." Those who seek him earnestly will discover him to be the only source of life, the truly Living One, the only one who can relate to them by his revealing of himself to them through faith in his Son who gives everlasting life to those who have a living faith in him. It is a work of the Holy Spirit. This touches on the matter of 'relation' which you also ask about.

However, an answer here can only ever touch on such matters, and there is a certain futility in even trying to answer such a question. Those who appreciate the awesomeness of the undivided, and indivisible, living God can have an experience of him as such which those who are in awe of mystical rituals, religious performances, and repeating formulas, might put in the place of entering into experience of God, due to having their minds corrupted from "the simplicity that is found in Christ - 2 Corinthians 11:3. It is too easy to allow desire for a 'head-trip' and/or an emotional experience to fool one into thinking they have actually experienced the living God, when they have not. Jesus warned that there is only one way to go, and that is to find the small, contracted, strait, narrow gate (Luke 13:24). It leads to life, to salvation. Jesus is that gate, that way (Matthew 7:13).

The living God in both testaments is just that...the God who is alive. This is over against all the gods of idolatry, the gods of wood and stone

And there ye shall serve gods, the work of men's hands, wood and stone, which neither see, nor hear, nor eat, nor smell. - Deuteronomy 4:28

These are Gods of the human imagination and they are not real...they do not have life...they are not living gods.

The living God is alive and the tri-unity of God is not excluded by an adjective which ascribes life.

So also with the Christ. If the Christ is reckoned as the eternal Son, eternally begotten of the Father and one in being with the Father (as trinitarians do reckon from Scripture) then this Christ is also living God.

Just as the Scribes and Pharisees understood Jesus' claim of equality with God from his statement "My Father worketh hitherto, and I work. (- John 5:17b)" because the claim literally is "the father of me":

Therefore the Jews sought the more to kill him, because he not only had broken the sabbath, but said also that God was his Father, making himself equal with God. - John 5:18

So we may also recognize, in the living God, both Father and Son as equal in ontology and distinct in person and, rather than seeking to kill Him, we may receive Him as both Lord and God.

That all men should honour the Son, even as they honour the Father. He that honoureth not the Son honoureth not the Father which hath sent him. - John 5:23

That is...the Son (of eternal Deity) not created as Adam but begotten by a Father (eternal Deity): Like begetting like as is the pattern demonstrated to us in all of creation. Jesus is that Christ, come in the flesh to reconcile flesh and Deity.