Adam became a living soul when God breathed into the physical elements that comprised Adam. He became a living soul. I don't see that as hyperbole and I have no idea why you would, unless it has something to do with you believing that God is not alive? How can God then breathe life into inanimate objects if He is not alive Himself? Genesis makes no distinction between the breath in man and the breath in all the flesh of the earth, meaning animals as well as man, anything with the breath of life, that life comes from God. It is the life that God has breathed into them. The exact word from chapters in Genesis makes no distinction between man and animal as far as the breath of life is concerned.
Yes he did, as did all human beings, but animals are not living souls they are strictly alive. Just as people in hospitals with no brain activity are basically alive but their soul has departed. What God breathed into Adam was both life and soul. God didn't breathe into anyone else or anything else.
The Bible says God is love, not God is life, but as he is omnipotent then he was able to create life as he did on Earth. Now it is commonly understood that God's creation came from his words and not from any existing thing so obviously God was not a life if he created life. There is like nowhere in the universe but on Earth and in Jesus.
Genesis does make a distinction because God only breathed into Adam, but you assume that just because life is called the breath of life in animals that God breathed into them as well but the scripture does not state that so you're assuming.
You cannot draw a precedent from silence.