Well yes, but not here. While "googling" is generic, it's still a specific narrow term and it does not mean "search".
Yeah, I might use “googling” to mean generic web search in everyday language, but I wouldn’t use it to refer to a site’s internal search function, and I wouldn’t use it at all in a technical description of some software.
you might not, but clearly the author does.
Right. If that wasn't the case, this comment chain calling that word choice by the author as unfortunate wouldn't exist.