What is the biblical basis for the belief that the soul/spirit continues after death? What scriptural support is used to defend the belief that the soul/spirit of man continues on after death?  And how does that work with the fact that God made man "from dust you are and dust you will return"?

If the question is seen as "too broad" I am mainly interested in the Catholic and/or Anglican understandings.
I think there is a biblical basis for believing that the soul/spirit is not extinguished when the physical body dies and is buried.  The words spirit and breath are translations of the Hebrew word ‘neshamah’ and the Greek word ‘pneuma’. The words mean “strong wind, blast, or inspiration.” Neshamah is the source of life that vitalizes humanity. “The Spirit of God has made me; the breath of the Almighty gives me life” (Job 33:4). It is the intangible, unseen human spirit that governs man’s mental and emotional existence. The apostle Paul said, “Who among men knows the thoughts of a man except the man’s spirit within him?” (1 Corinthians 2:11). Upon death the “spirit returns back to God who gave it” (Ecclesiastes 12:7; see also Job 34:14-15; Psalm 104:29-30).

All human beings possess both material (physical) and immaterial (spiritual) characteristics. Each person has a physical body. The New Living Translation Bible says that after God formed Adam from the dust of the ground “He breathed the breath of life into the man’s nostrils, and the man became a living person” (Genesis 2:7).  The King James Versions says man was created as a “living soul.”

The word soul can refer to both the immaterial and material aspects of humanity. Unlike human beings having a spirit, human beings are souls.  The Bible nowhere says that God’s breath is imparted to other animals.  Only humans are “formed in God’s image” (Genesis 1:27) and have spiritual awareness and moral conscience (Job 32:8).

The soul and the spirit are the immaterial parts that the Bible ascribes to humanity.  Whenever the word spirit is used in the Bible, it refers to the immaterial part of humanity that “connects” with God, who is spirit (John 4:24). The soul and the spirit are connected, but separable: “For the word of God is alive and powerful. It is sharper than the sharpest two-edged sword, cutting between soul and spirit, between joint and marrow.  It exposes our innermost thoughts and desires” (Hebrews 4:12).

The soul is the essence of humanity’s being; it is who we are. The spirit is the immaterial part of humanity that connects with God.  The soul, as the life essence of the body, is removed at the time of physical death: “And as her soul was departing (for she was dying), she called his name Ben-oni; but his father called him Benjamin” (Genesis 35:18 KJV). The NLT says Rachel, who was about to die, named the baby with her last breath. The NIV says she breathed her last.

This begs the question, where was Rachel’s soul/breath/spirit departing to? Her body went into the ground to remain there until the resurrection, but what of her soul? Ecclesiastes 3:20-21 explains how the dead go to the same place (into the ground): “all come from dust, and to dust all return. Who knows if the spirit of man rises upward and if the spirit of the animal goes down into the earth?” Ecclesiastes 12:7 says that the “dust returns to the ground it came from, and the spirit returns to God who gave it.”

Elsewhere in the Bible, it speaks of the souls of those whose bodies have died, yet they live!  Revelation 6:9 speaks of “the souls of those who had been slain” who were under the altar in heaven.  Revelation 20:4 describes how “the souls of those who had been beheaded because of their testimony for Jesus” were seated on thrones in heaven.

Please note that the human soul it is not eternal in the same way that God is. God is the only truly eternal being in that he alone is without a beginning or end. God has always existed and will always continue to exist. All other sentient creatures, whether they are human or angelic, are finite in that they had a beginning. While I believe that human souls will live forever after they come into being, the Bible does not support the concept that our souls have always existed. Our souls are immortal, as that is how God created them, but they did have a beginning; there was a time they did not exist.

Not all Christians believe in the soul/spirit of man continuing to exist after the death of the body.  Some believe in “soul annihilation.”  However, whilst related to the question of the soul, it is outside the scope of this question and is for others to defend if that is what they believe.