Yes sir I fully agree they died spiritually (lost their relationship with God) when they ate, and later they literally died.
Yes, we agree about the various aspects of death, but you claim souls die when the body dies, that it was that kind of death God said would happen to Adam and Eve.
To make that "true" you change the meaning of "day" to refer to a long period of time.
But context reveals it is idiom and means "immediately when you eat you will die spiritually because you will no longer exist in "God's presence".
2 And the woman said to the serpent, "We may eat the fruit of the trees of the garden;
3 "but of the fruit of the tree which is in the midst of the garden, God has said,`You shall not eat it, nor shall you touch it, lest you die.'"
4 Then the serpent said to the woman, "You will not surely die.
5 "For God knows that in the day you eat of it your eyes will be opened, and you will be like God, knowing good and evil."
6 So when the woman saw that the tree was good for food, that it was pleasant to the eyes, and a tree desirable to make one wise, she took of its fruit and ate. She also gave to her husband with her, and he ate.
7
Then the eyes of both of them were opened, and they knew that they were naked; and they sewed fig leaves together and made themselves coverings.
8 And they heard the sound of the LORD God walking in the garden in the cool of the day, and
Adam and his wife hid themselves from the presence of the LORD God among the trees of the garden. (Gen. 3:2-8 NKJ)
Right after they ate they died and in the realm of spiritual death "their eyes were opened to the evil raging in their fallen nature".
How shameful their naked bodies now were compared to the holiness they once had when spiritually alive in God's presence:
It was "spiritual death/separation from God's presence" He said they would die after they ate, not death of their souls HUNDREDS OF YEARS LATER:
For as in Adam all die, even so in Christ all shall be made alive. (1 Cor. 15:22 NKJ)
1 And you He made alive, who were dead in trespasses and sins,
2 in which you once walked according to the course of this world, according to the prince of the power of the air, the spirit who now works in the sons of disobedience, (Eph. 2:1-2 NKJ)