What is the ruling on describing a person or animal as "mine" (مِلْكٌ لي), with the intention of controlling them and not for worship, as in a husband's statement to his wife: "You are mine" (أنتِ مِلْكٌ لي)?

A person owns by virtue of Allah granting them ownership. Therefore, their ownership is not absolute, and they dispose of what they own according to what the Sharia has permitted. And the husband's statement to his wife, "You are mine," is permissible, and it indicates that he has the right to enjoy her exclusively, and no one shares in that with him. This is not polytheism (shirk). One must also be wary of obsessive whispers (waswas).