Did writing a book give you an edge at a big company, or opened up possibilities? If so, how and what?
I received a few offers for jobs at small startups using Rust, where the ones making the decisions regarding recruitment (CEO/CTO) have a technical background.
But, I believe that a book is not the best way to have the edge that you are looking for. Building an audience (blog/newsletter/YouTube/twitter...) would, in my experience, bring better results. An audience is composed of people. Some of these people work in big companies. So the day you are looking for a new job, they may help accelerate the HR process as they already know the quality of your work.
A book, on the other hand, is almost static, you cannot use it to your full advantage at the RIGHT moment (when you are looking for a new job).