Bible translations can be confusing when they translate the same word to multiple different meanings.

God brought Adam, and all the animals, to life by causing them to start breathing. Thus Adam became a living soul once he had started breathing and his lifeless body started functioning.
Genesis 35:18 (WEB):
(18) As her soul was departing (for she died), she named him Benoni, but his father named him Benjamin.
This verse doesn't say anything about people continuing to live after they have died (which is a contradiction of what it means to be dead - if you continue to live after you have died, then you have not died!). The Hebrew word translated as soul is
nephesh, which means 'a breathing creature' (it comes from the root word
naphash, meaning 'to take breath, refresh oneself'), and it has been translated as soul, self, breath, life, creature, person, appetite, mind, living being, desire, emotion, passion, and other meanings. In the above verse it is more logically translated as the GNB renders it:
(18) But she was dying, and as she breathed her last, she named her son Benoni, but his father named him Benjamin.
1 Kings 17:21-22 (WEB):
(21) He stretched himself on the child three times, and cried to Yahweh, and said, “Yahweh my God, please let this child’s soul come into him again.”
(22) Yahweh listened to the voice of Elijah; and the soul of the child came into him again, and he revived.
Again, these verses don't say anything about people continuing to live after they have died, and the word translated as soul is
nephesh. It should be more sensibly translated as:
1 Kings 17:21-22 (GNB):
(21) Then Elijah stretched himself out on the boy three times and prayed, "O LORD my God, restore this child to life!"
(22) The LORD answered Elijah's prayer; the child started breathing again and revived.
or ESV:
(21) Then he stretched himself upon the child three times and cried to the LORD, “O LORD my God, let this child's life come into him again.”
(22) And the LORD listened to the voice of Elijah. And the life of the child came into him again, and he revived.
God breathed the "breath of life" (not His spirit, or breath, for God does not breath air), and then the animated Adam is referred to as a "living creature". He becomes a living soul, not a soul living in a body:
Genesis 2:7 (WEB):
(7) Yahweh God formed man from the dust of the ground, and breathed into his nostrils the breath of life; and man became a living soul.
Genesis 2:7 (ESV):
(7) then the LORD God formed the man of dust from the ground and breathed into his nostrils the breath of life, and the man became a living creature.
Genesis 2:7 (TLV):
(7) Then Adonai Elohim formed the man out of the dust from the ground and He breathed into his nostrils a breath of life—so the man became a living being.
It's confusing because in the New Testament it uses the word 'soul' as that part of our being which lives in the body - Matthew 10:28 (WEB):
(28) Don’t be afraid of those who kill the body, but are not able to kill the soul. Rather, fear him who is able to destroy both soul and body in Gehenna.
As the Online Bible Greek Lexicon puts it, the word
psuche that is translated as soul, can refer to "the seat of the feelings, desires, affections, aversions (our heart, soul etc.)". I regard that as a spirit part, i.e. it cannot be killed/destroyed by any physical means, and only God can destroy it.
In the Bible, the only earthly beings that are promised the possiblilty of a home in heaven are Christians, believers in and followers of Jesus the Messiah, and they will be given a spirit body and become part of a new creation of God (2 Corinthians 5:17), and will share in our Messiah's inheritance from God. That's why they have to become spirit beings and live in heaven, in order to inherit God's Kingdom - 1 Corinthians 15:50 (WEB):
(50) Now I say this, brothers, that flesh and blood can’t inherit God’s Kingdom; neither does the perishable inherit imperishable.