The concept of soul as an immaterial part separate from the human body does not exist in the Bible but was adopted into Christianity from Greek philosophy.
In Old Testament (OT) the Hebrew word that is commonly translated "soul" (but, depending on translation, sometimes as "living soul", "living creature", and other variants) is "nep̄eš". This is the word used in locations such as Genesis 2:7 (KJV) to refer to humans:
And the Lord God formed man of the dust of the ground, and breathed
into his nostrils the breath of life; and man became a living soul.
And in locations such as Genesis 2:19 (KJV) to refer to animals:
And out of the ground the Lord God formed every beast of the field,
and every fowl of the air; and brought them unto Adam to see what he
would call them: and whatsoever Adam called every living creature,
that was the name thereof.
(reference below)

In the same manner the New Testament (NT) uses the term "psykhe" to refer to a person as a living being. For example, Romans 11:3 says:
Lord, they have killed thy prophets, and digged down thine altars; and
I am left alone, and they seek my life.
(reference below)

The New Catholic Encyclopedia (1967), Vol. 13, p.467 says in the article SOUL, HUMAN, IMMORTALITY OF as follows (emphasis added):
The soul in the OT means not a part of *man, but the whole man - man as a living being. Similarly, in the NT it signifies human life: the
life of an individual, conscious subject...Consequently, for the
Israelite, man dies when his nepeŝ leaves him..., and death is somehow
a diminution of life, a loss of life. The NT remains faithful to
this understanding of death.
(reference provided below)

Likewise, the same encyclopedia says in Vol. 4, p.669, in the article DEAD, THE (IN THE BIBLE) that ancient Israelites
did not regard man as a loose composition of a material element (body)
and an immaterial element (soul), as Greek philosophy did....Death was
not regarded as a separation of two distinct elements in man, as in
Greek philosophy; the breath of life departs and man is left a "dead
being"
(reference provided below)

This same encyclopedia also attributes the development of the concept of an immortal soul to Middle Platonism. In Vol. 13, p.454, the following is said in the article SOUL, HUMAN (emphasis added):
The resulting doctrine of the soul as a substance made for union with the body, yet subsistent in itself, rational, incorporeal,
simple, and immortal, was far different from the teachings of the
early Greek philosophers. Plato and Aristotle seem to have had little
direct influence in the formation of such a concept; when their
doctrine was adduced, it was usually subject to criticism.
Neoplatonism received less attention than one might expect. It is
more probable that Middle Platonism, which flourished in the first
Christian centuries, furnished Clement, Origen, and later writers with
key ideas.
(reference provided below)

As the New Catholic Encyclopedia admitted (above), the notion that a human person has a soul (let alone an immortal soul) is not found in either the Old Testament or the New Testament. This is because even the apostles, who had been trained by Jesus, believed in the same concept of afterlife as did Moses and the Old Testament prophets.
The ideas that a person has a separate soul, and the later addition that the soul is immortal, were developed long after the death of the apostles. Writers such as Clement and Origen based these ideas not on the Bible but on pagan Greek philosophies.