I tried to find how Judaism looks at Spiritual Death and couldn't find anything, it seems to be a solely Christian doctrine?
If so, the ancient Jews held the position - the reason we die is because we are sinners, no further strings attached just read Genesis at face value. Genesis is the revelation of the ONE God in the middle of a saturated world of polytheism answering the big questions, among that the question - why do we die? [A] because we are sinners. Moses wanted to see God's glory and His answer was - And he said, Thou canst not see my face: for there shall no man see me, and live. Hence God withdraw from His creation.
Spiritual Death is not mentioned in Scripture, it's a doctrine derived from Scripture passages and it strikes me as odd Judaism missed it. And so I like to play the role (for a while) that Spiritual Death is not a sound doctrine (against better knowing) for the sake of a good discussion.
Gen 2:17 - but of the tree of the knowledge of good and evil you shall not eat, for in the day that you eat of it you shall surely die.
They ate and died.
Death = Death.