How to understand the relationship between God’s governing activity and sin?
Without understanding what, exactly, you mean by “God’s governing activity” I went and searched this question and I think this may be helpful.
God is sovereign, but He did’t create evil. Satan changed to be evil, because God of love gave the freedom. As creations we need to use the freedom to love back to God freely and willingly, but not go astray from God. That’s so sad for God.
Sadder for us! It does not harm God if we do not turn to Him. But it costs us EVERYTHING if we don’t.