‘seed’ - ‘זֶרַע’ - zeraʻ, is always singular. This is ‘by design’. The first occurrence of the word helps explain why ....
GEN 1:11 Then God said, “Let the earth bring forth grass, the herb that yields seed, and the fruit tree that yields fruit according to its kind, whose seed is in itself, on the earth”; and it was so.
Everything starts with seed. Whether natural, or spiritual. The first parable both explains the importance of ‘seed’, and the ‘spiritual connotations. (Matthew 13). And Jesus says in Mark 4 ...
MARK 4:13 And He said to them, “Do you not understand this parable? How then will you understand all the parables?
This principle of ‘seed’ is crucial to understanding much. Importantly, the ‘word’ [of God] is ‘seed’. We [believers] are ‘born again’ by or through the word of God. Saved by the word!
But back to your Q, here is the concept of reproduction, and the reason for singularity ... “whose seed is in itself,”
It ties in very tightly with the Hebrew concept of ‘oneness’ - ‘echad'’, hence the ‘singularity’ of ‘zera’’
Now to the second part of your answer - and up front, this view is not the traditional view, so I not only add this caution, but also expect reaction.
The ‘seed’ of the serpent is Adams offspring. Specifically Adam. Adam had ‘eaten’ from the tree, his spirit was dead. Adam was warned he would die the day he ate. Adam was separated from God. The result of what the serpent did would be passed on via Adam - to all. How does something, how does anything get ‘passed along’, or passed down? - via seed! And through this, via his ‘seed’, all are born in this state - separated from God.
Hence man needs the Word [seed] in order to be ‘born again’. To ‘re-create’ that which came from Adam, to that which comes by Christ.
It is Jesus who [can] reunites man back to his Father, back to God. He is the ‘first fruit’, and we can partake of his ‘seed’.
The enmity is clear, right from the start. Man naturally rebelling, resisting. Man needs to make a choice to deny ‘self’ and accept God. That battle Paul outlines in Romans 9. Between the old man, result of Adams ‘seed’, and the new man, born again from another seed.
Not sure whether you were also asking about the ‘seed of the women’. This is accepted by most to be referring to Jesus. Women have no seed, no ‘seed’ comes from them - hence the first [veiled] reference to a virgin birth. The virgin birth could not have occurred unless it was prophesied. And Isaiah does this. Prophecy is ‘Gods Word’. Because, as per the parable above, Gods Word is [the] seed. Jesus’s birth needed a seed, just like any birth - natural or supernatural!