If God was walking in Gen 3:8, this implies he had a body, which seems to contradict the notion of his spirituality, or at least supports the idea that he had a body. Correct?

It’s complicated; this suggestion is somewhat misleading. We have many other examples of God’s appearing in some sort of visible form—called a theophany—but that does not mean that is in some sense the form of God himself, as if God were limited by having a body. Moreover, God said, “there shall no man see me, and live” (Ex 33:20). Yet the human-appearance face of God, in theophanies, was shown to people, most famously that of Jesus, but also to Abraham in Gen 18, and here to Adam and Eve—and the people did not die. So we must conclude that there was some other more literal “face” of God that it was indeed deadly to see; it would be an encounter with God, directly before the presence of God, as he is in himself. Isaiah seems to have had such an encounter at the beginning of his prophetic career, and when he saw the Lord, he said, “Woe is me! for I am undone; because I am a man of unclean lips…for mine eyes have seen the King, the Lord of hosts.” As if to underscore the truth of this, a seraph gives him special permission to stand in the Lord’s presence: “having a live coal in his hand, which he had taken…from off the altar: and he laid it upon my mouth, and said, Lo…thy sin is purged.” (Isa 6:5-6) And, particularly because Adam and Eve were then in their sin, the walking, apparently bodily God had to have been a theophany that failed to reveal God’s true nature—or else Adam and Eve would have been destroyed. That is, they would have been destroyed unless, being sinless, they were able to look upon his face; but then, after they sinned, God confronted them in the Garden, and they were not instantly destroyed. So it is likely that it was, again, a theophany that they saw, one that did not reveal God’s true nature.