If you’re using regex I’m assuming you know of utilities like Regex 101 to check your syntax.
With JS-styled regex the entire statement is enclosed in slashes. /parent:: $/ should have the desired effect here.
I second DataView for these kinds of tasks as the plugin revolves around YAML frontmatter. I have a utility note called “notes with cleanable metadata” that has a bunch of these DataView queries that update in real time.