Official English volumes (J-Novel Club) are high quality, but they lag behind the Japanese web novel (Shosetsuka ni Naro) and physical publication. "Raw new" often refers to the latest web novel chapter posted by the author, hours after it goes live.
Part 4 introduces many new characters (like Hannelore and Prince Anastasius) whose designs are highly anticipated. How to Navigate Raw Chapters honzuki no gekokujou part 4 raw new
For the Light Novel version (which includes beautiful illustrations by You Shiina and extra chapters not found in the web novel), TO Books is the official Japanese publisher. They often release previews and digital "new" chapters for purchase. Official English volumes (J-Novel Club) are high quality,