>>> Do not eat of the tree.... It was a Kosher Law, about what to eat. One could then deduce that it matters to G-d what you eat.
Before they sinned, there was no “Law” except that of sin and death. The sin was not in the eating so much as it was disobedience and abandonment of God (Satan told them they could be like God if they ate it)
As far as deducing things, there is no need here, because we see clearly that the fruit of this particular tree had physical attributes which directly affected man’s spiritual and physical attributes. The fruit literally gave them the knowledge of good and evil. This is something they were NOT ready for, and in their sin they corrupted their flesh.
The tree of life as well had physical/spiritual qualities that would have rendered them irreconcilable if they had eaten of it as well, once they were corrupted. This is why God in His mercy drove them out of the garden lest they eat of it.
Kocher laws (what we should or shouldn’t eat) pertains to “unclean” food which represents a risk to physical health.