I have heard some Christians claim that Satan was able to make Eve eat the fruit because she added to God's word. For me to agree with that accusation I would need a verse that said God or Adam told her not to eat of the tree. Nowhere is there any verse that states just how Eve heard of the restriction. Minus that, to accuse her of adding to God's word is bearing witness against her without all the facts. I agree that Adam may well have told her to not touch the tree.
In your post you state that “when Eve sinned” and the context is she sinned by eating the fruit. Let's see if God agrees with that statement.
Genesis 3:14 So the Lord God said to the serpent: "Because you have done this, …....... NKJV
God blamed the Serpent for his part in the event.
Genesis 3:17 Then to Adam He said, "Because you have heeded the voice of your wife, and have eaten from the tree of which I commanded you, saying, 'You shall not eat of it': NKJV
God blamed Adam because he obeyed Eve's voice instead of heeding God's warning concerning eating fruit from the tree.
Genesis 3:16 To the woman He said: "I will greatly multiply your sorrow and your conception; NKJV
He tells her that for her childbirth will now be in pain and her husband will now rule over her. I do not see any because in the statement God made to her.
She ate the fruit first.
Romans 5:13 (For until the law sin was in the world, but sin is not imputed when there is no law. 14 Nevertheless death reigned from Adam to Moses, even over those who had not sinned according to the likeness of the transgression of Adam, who is a type of Him who was to come. NKJV
The Holy Spirit states that Adam sinned.
Romans 8:20 For the creation was subjected to futility, not willingly, but because of Him who subjected it in hope; 21 because the creation itself also will be delivered from the bondage of corruption into the glorious liberty of the children of God. NKJV
When Adam sinned all of creation fell into sin. God subjected the world to futility when Adam sinned, which could explain what happened to Eve after the fall.
1 Timothy 2:14 And Adam was not deceived, but the woman being deceived, fell into transgression. NKJV
The Holy Spirit agrees that Eve was deceived and fell into sin. By Romans 8: 20 all of creation fell into sin.
Without supporting scripture, I will not accuse Eve of sinning because she ate the fruit.