I am glad to see you inching towards Covenant Theology. However, there is one major difference between the covenant between God and Adam, and the Sinaitic Covenant. The latter had an elaborate system of sacrifices which allowed God to pass over the sins of the Israelites until the one perfect sacrifice of Christ.
However, there was no arrangement to deal with the sin of Adam.
'.....for in the day that you eat of it, you shall surely die.' that's it; no arrangement to take away sin. In Genesis 2:25 we read,
'And they were both naked, the man and his wife, and were not ashamed.' What does this mean and why does the Holy Spirit bother to tell us? Because we are to understand it theologically. Adam and Eve had no covering. There was no arrangement to cover sin. But that didn't matter because there was no sin. The couple came sinless from the hand of God who made them and pronounced what He had made
'very good.'
But as soon as they fell into sin, Adam and Eve were troubled by their nakedness. They knew that they had no covering, so they tried to make one themselves. But a man-made covering is worthless to hide one's sins (Isaiah 64:6) -- no more than a fig leaf.
God saw right through it. The only covering for sin that satisfies the righteousness of God is the righteousness which He provides in Christ (c.f. Isaiah 61:10).
But the point is that Adam and Eve needed no covering before the fall simply because they were sinless. They were also spiritually alive because they were created by Christ (John 1:3) and so they walked with God..