God did not stop loving man. Man turned away from God. Adam could not even take responsibility for his disobedience. "The woman you gave me....." And Eve blamed the devil.
I see how the rabbit hole deepens. There seems to be an entire theology built around this idea that death is separation from God in order to ultimately make death not death, but instead eternal life in eternal pain. Thank you for sharing that, I do make it a point to understand all doctrines even when I am 100% sure they're wrong.
I digress, there is actually a verse for sin separating people from God and it's Isaiah 59:2. "Separation" from God does not mean someone is literally hidden from God in some place He can't find them or reach them. Separation from God means that God is going to literally not listen to you anymore the Bible often refers to this as God "hiding His face."
Sin is utterly detestable to God and offensive, if someone is separated from God it means their sin has offended Him. As you said, God does love people even though we can be so offensive, He'll eventually come back around, praise God.
Death is actually just death, but there is spiritual death, soul death, and physical death. If by death being separation from God they are destroyed then yes I agree, but death isn't living eternally out of God's presence.