Let me start with what the skeptics get right: "topical authority" is not a term Google uses. You will not find it in any patent filing, algorithm update announcement, or official documentation. It is a label the SEO community invented to describe something we observed: sites that cover a subject comprehensively tend to rank better for every page in that cluster than sites that publish one-off articles.
That observation is real. But calling it "topical authority" and treating it like a button you press is where things get murky.
If you hang out on Reddit's SEO communities, you will find plenty of people who call topical authority a myth. Their argument usually boils down to: "I published 50 articles on one topic and nothing happened." And they are often right, because what they built was not authority. It was volume. Those are different things.
What Google actually says
Google has described several systems that reward topical depth. Their helpful content system evaluates whether a site has a "primary purpose or focus." Their E-E-A-T guidelines explicitly ask whether the content creator has demonstrated expertise and experience in the subject. Their information gain patent describes rewarding content that adds new information to the corpus on a topic.
None of this is called "topical authority." All of it adds up to the same thing: Google rewards sites that demonstrate comprehensive, genuine expertise on a subject. Whether you call that topical authority or "doing a good job covering your niche" is semantics.
My honest assessment
Topical authority is real as a concept but overhyped as a tactic. It is not a magic lever. It is the cumulative effect of doing several things well: covering a topic thoroughly, interlinking your content intelligently, earning backlinks from relevant sources, and publishing content that actually helps people. If you do all of those things, you will rank better. If you just publish 50 thin articles and call it "building topical authority," you will not.