I can’t speak directly to the trade press process, but in academia, there is absolutely a process of peer review for historical books and articles. The first step is submitting a book proposal to a publisher, of course, but if the proposal is accepted, the manuscript goes through several rounds of reviews and edits before being published. This usually involves the manuscript being sent out to other scholars who have expertise in the subject or a related field. Your editor will find reviewers and request that they assess the book. I’m not sure if it varies by publisher whether or not these reviews are blind (it can be kind of hard, as academia is small and we often know what major projects others in our field are working on), but typically it takes about a year to a year and a half from the time of submitting your completed manuscript to publication, to allow for comments, editing, etc.

In academic journals (shorter articles) the process is even more rigorous, and almost always entails a “double-blind” style review where neither reviewer nor reviewee are known to each other. Reviewers then recommend the piece be published, revised and resubmitted (with comments on what is missing), or rejected (with comments on why - was it misleading, does it commit factual errors, does it add nothing new, etc).

It’s all done pretty informally. For example, I was recently asked to review an article by the editor of a Journal, as the article references my work. While this reference was left in the copy I received (when references are both obvious and critical to the argument they are left in), all other references are removed to prevent people from making decisions based on who cites who, rather than the quality of the argument.

You can get at your question indirectly be reading the /u/caffarelli perennial How to Judge a Book Without Even Reading It and a thread about how to find secondary sources

/u/flyingdragon8's answer to How do you find trustworthy books and avoid bad history? may also be helpful to you.