Yes, writing a book about overcoming depression and anxiety through self-help can indeed make someone an author. In the literary world, an author is simply someone who has written a book or other literary works. Publishing a book, regardless of the genre or topic, grants the authorship title to the individual who wrote it.
Authorship is not limited to specific themes or genres; it includes fiction, non-fiction, self-help, poetry, academic works, and more. Writing a book on a topic as important and impactful as overcoming depression and anxiety through self-help can be a significant achievement, and the author can contribute to helping and inspiring others who might be facing similar challenges.
It's worth noting that the process of becoming a published author involves more than just writing the book. It also entails finding a literary agent or publisher, going through the editing and publishing process, and then promoting and marketing the book to reach its target audience. But regardless of the publication method (traditional publishing or self-publishing), the act of writing a book is a notable accomplishment that makes someone an author.