It looks like INSERT INTO ... RETURNING allows defining a target for the returned values like SELECT ... INTO does.
This could be mentioned in the synopsis, or at least in the description of "output_expression", maybe even garnished with an example.
That isn't how it works. RETURNING simply turns INSERT into a result set producing SQL Command. And SQL doesn't have a concept of "target" (variables) in the sense you are thinking. pg/pgsql does, allowing result set data to be placed into variables.
If you look you'll notice a corresponding lack of "INTO" on the SELECT Command reference page as well, for the same reason.