What kind of death did Jesus experience?
In order to explore this question from the text, we need to put aside personal beliefs for a moment - including doctrine on the Trinity or preconceived ideas about heaven and hell, the soul, etc.
The Greek word γεύομαι can be translated as 'to taste', but also ‘to eat’ and more generally ‘to experience'. It is not specifically a small or partial experience, so we cannot assume that what is meant here is only a small taste of death.
All written accounts of Jesus say that he died - ie. that his physical body became void of life. His body was then buried, and from that point Jesus no longer enjoyed a material existence.
These written accounts also describe, in a number of ways, the experience of Jesus’ presence being lost to the world for a short time after this death, before it was restored just three days later - not necessarily as a material body, but as the faithful began to 'experience' him or to witness him 'appear' amongst them.
During those three days - regardless of whether one believes in heaven or hell, in a soul, the Trinity or the serpent - all accounts point to a death experienced by Jesus in every sense of human experience. For those three days, Jesus was lost to the living human experience in every way - body, soul and spirit.
While we may ‘know’ that God cannot cease to ‘exist’ spiritually, all accounts attest that for three days no one, not even those closest to him were able to experience Jesus at all except as a loss - a void. We can theorise about what goes on beyond our human experience, based on what we believe, but in the end we can only attest to the human experience itself.
But Jesus is experienced as alive
We also don't need to believe in the resurrection, in heaven and hell or the Trinity to recognise that, after those three days, Jesus has continued to exist as a non-material presence at least somewhere in human experience, whether or not we recognise that presence as ‘real’ or ‘alive’, ‘human’ or ‘God’, or simply a character in a book.
The way I see it, after three days his disciples began to recognise that this spiritual connection Jesus had nurtured in their personal experience of his life did not cease to exist - it was only their awareness of it that was temporarily experienced as ‘lost’. This spiritual or non-material element of human experience, and its ability to connect beyond time and space, was what he had been teaching them to focus on all along. And whenever they then brought those diverse experiences together, Jesus appeared as very much a 'living', active presence amongst them: bringing peace, reminding them of what he had taught and what he had suffered in order to demonstrate the eternal, spiritual element of human experience by his example.
What does this text teach us?
As for what Hebrews 2:9 intended to teach, we know that Paul is writing specifically to the Jewish in his community, and has been arguing the significance of Jesus to scripture. So far in this letter he has cited a number of scriptural passages to illustrate that Jesus is both a subject of scripture and ranked above the angels. Here he gives a small interpretive twist to Psalm 8, which in the original text describes 'the son of man' as made 'little less than God (Elohim)' and crowned with glory and honour, with all things put under his feet:
what is man that thou art mindful of him, and the son of man that thou dost care for him? Yet thou hast made him little less than God, and dost crown him with glory and honor. Thou hast given him dominion over the works of thy hands; thou hast put all things under his feet (Psalm 8: 4-7)
Paul instead phrases this part of the text in the past tense as 'lower than the angels (angelous)' for a 'little while', and only now crowned with glory and honour:
It has been testified somewhere, "What is man that thou art mindful of him, or the son of man, that thou carest for him? Thou didst make him for a little while lower than the angels, thou hast crowned him with glory and honor, putting everything in subjection under his feet.” (Hebrews 2: 6-8)
With this slight twist, he suggests that Jesus fulfills this scripture - by allowing himself to be temporarily placed below the angels (to become mortal, to experience death for the benefit of all) for a time in order to attain glory greater than that of the angels (whom he has already described as servants of those who attain salvation).
But the original Psalm describes a present glory and honour bestowed on 'the son of man', proclaimed by David. It was not until people witnessed Jesus demonstrating the potentiality of this 'dominion over the works of thy hands' that we would even begin to understand our own spiritual potentiality as ben-adam, as the offshoot of humanity that walks with God as described in the OT. In this way the original scripture is indeed fulfilled by Jesus - just not in the limited way that Paul described in addressing the Hebrew members of the church. The potential for glory and honour is available to every ‘son of man’ - all those who walk with God.
Does Acts 2:27 say that the soul of Jesus went to hell?
Peter also twisted the meaning of scripture to suit his agenda when he addressed the Jewish crowd in Acts. Here he quotes Psalm 16, where David speaks of the security in the Lord of his heart and soul as well as his body.
Therefore my heart is glad, and my soul rejoices; my body also dwells secure. For thou dost not give me up to Sheol, or let thy godly one see the Pit. Thou dost show me the path of life; in thy presence there is fulness of joy, in thy right hand are pleasures for evermore. (Psalm 16: 1-11)
Peter then attests that, because David is dead and buried, he must not have been talking about himself, suggesting that he was prophesying instead:
Brethren, I may say to you confidently of the patriarch David that he both died and was buried, and his tomb is with us to this day. Being therefore a prophet, and knowing that God had sworn with an oath to him that he would set one of his descendants upon his throne, he foresaw and spoke of the resurrection of the Christ, that he was not abandoned to Hades, nor did his flesh see corruption. (Acts 2: 29-31)
But did David expect anyone to be permanently or eternally kept alive, or only presently? He begins this Psalm with ‘Preserve me, O God, for in thee I take refuge’, suggesting that this song is in reference to himself in the present tense: his experience of having heart, soul and body preserved. Once again, though, the scripture is nevertheless fulfilled by Jesus - as it is only through his teachings and his example, his death and his disciples recognising that he is alive for them and for others beyond material existence, that ‘the path of life’ and ‘fullness of joy’ that David says he was shown in keeping the Lord always before him is fully realised and shown to all those who believe: as a spiritual path of eternal life.
So, whether or not we believe in the concept of ‘Sheol’ as a place where this spiritual element of the human experience goes after death to await ‘the Pit’ as the ultimate end of existence on the Day of Judgement, what David expressed in terms of his own experience of walking with God is later expressed more fully in the life of Jesus.
And what about the serpent?
The verse of John 3:14 associates the resurrection with Moses lifting a serpent:
Truly, truly, I say to you, we speak of what we know, and bear witness to what we have seen; but you do not receive our testimony. If I have told you earthly things and you do not believe, how can you believe if I tell you heavenly things? No one has ascended into heaven but he who descended from heaven, the Son of man. And as Moses lifted up the serpent in the wilderness, so must the Son of man be lifted up, that whoever believes in him may have eternal life. (John 3: 13-15)
First of all, it’s important to note that these verses are not the words of Jesus, but of John, the gospel author (there are no speech marks in the original Greek text, so this is an easy error to make). While it begins with “Truly, truly I say to you”, the rest of verse 13 is written in first person plural (we), and repeated later in this same chapter in reference to John the Baptist, where a clear distinction is made between what John the Baptist speaks of (earthly things) and what Jesus himself speaks of (heavenly things):
He bears witness to what he has seen and heard, yet no one receives his testimony; (John 3:32)
While the OP associated this serpent reference with Numbers 21:9, it more closely refers to Moses lifting up the serpent in Exodus:
Then Moses answered, “But behold, they will not believe me or listen to my voice, for they will say, ‘The Lord did not appear to you.’” The Lord said to him, “What is that in your hand?” He said, “A rod.” And he said, “Cast it on the ground.” So he cast it on the ground, and it became a serpent; and Moses fled from it. But the Lord said to Moses, “Put out your hand, and take it by the tail”—so he put out his hand and caught it, and it became a rod in his hand— “that they may believe that the Lord, the God of their fathers, the God of Abraham, the God of Isaac, and the God of Jacob, has appeared to you.” (Exodus 4: 1-5)
So John 3:14 does not suggest that Jesus became like the serpent in relation to sin, but in relation to being a clear sign that God ‘has appeared to you’.
Sorry, I don’t have a neat and succinct explanation for these questions. I don’t think there is one. I only hope that I’ve helped clear away some of the clutter.
We continue to seek more tangible, verifiable answers to the question of existence beyond physical death. We can picture serpents or Sheol, heaven or hell, even a separate place of rest for the soul. All of these images seem easier to grasp in the human mind than what Jesus has taught and shown us (through sharing the human experience beyond words and pictures) about the true nature and potentiality of our spiritual and material existence, and of our relationship with God.
If it were that simple to explain with words, we wouldn’t need the whole bible or another two thousand or more years of human experience and expression to try and figure it out, would we?