I wonder when my manager "prompts" me "I want the feature X and I want it fast", is his prompt a human creativity?

To some extent yes. Your output at work is based on a combination of inputs from others in your organization, and is being paid for by your employer, so the organization owns the copyright on what you make for them.

I think from this view it makes sense that an LLM is a tool, and the operator of that tool (or their employer) can own the output.

The tricky part is when you squint and view an LLM with training input and prompted output as a machine that launders copyrighted input into customized output that is now copyrighted by a new owner.

A machine that vacuums up film reels and splices them according to a set of instructions by the user to create a compilation of recent animated Disney movies with the Shrek soundtrack superimposed would probably not pass legal challenges if the user of the tool attempted to claim full copyright on the output.