There are definitely different schools of thought on this!

I would say that writing a book is like playing a game of telephone. Whatever may be communicated intentionally or unintentionally, is not guaranteed to be received in the same form that it was transmitted.

Additionally most works have contrasting messages that can be potentially interpreted. If I'm analyzing HP in terms of class struggle and power dynamics, what I'm going to look for is whether audiences resonated with the plight of poor broomless Harry and the enslaved house-elves, or whether they resonated with sacrificing the oppressed to maintain the wizarding world's status quo. This could inform me about what these audiences feel about exploitation of individuals in states on the empire's periphery. The interpretations reflect the audiences biases, ideology, and other conditions. The author's own background often has a minimal influence on popular interpretations.

Finally, when looking at works, we often find that the popular version is only the latest of a series of very similar stories published by different authors over a number of years. We don't learn much by looking at each of these authors: We can learn a bit about the author, but nothing about why one work resonated with audiences and another did not. To understand more we must recognize that works are received differently based on the time, place, and culture in which they are released. This leads us to investigating the differences between each work's audience. Oftentimes an author is ahead of their time and they don't find success, whereas derivative (but similar) works are released after a culture shift and they do become popular. We can also study how a work is interpreted differently over long periods of time, which can be very informative about changes in society.

A fun example of some of this is Starship Troopers - the book and the movie. The book was not a major success; its lasting impact was to spawn a satirical movie that mocked the source material. Meanwhile the movie's satire was largely missed by bloodthirsty audiences contemporaneous to its release. Their interpretations were in contrast to the backgrounds of their respective creators. Perhaps the book would have been received better at the time the movie was published, and the movie would have been received better at the time the book was published!

You wouldn't be wrong to have a focus on the author, but fwiw I think you would be pigeon-holing your analysis and limiting its utility.