We're splitting hairs here, but both Wikipedia (https://en.wikipedia.org/wiki/A_Star_Is_Born_(2018_film)) and IMDB (https://www.imdb.com/title/tt1517451/) have it categorized as music/musical. I understand what you're getting it - it isn't a conventional "musical", but given the amount of time the characters spend singing, and how many musical numbers are in the film, it's not unreasonable to put it in the musical category.
The studios determine which category their films will run for when it comes to the Golden Globes, based on where they see the best chance to win. Unless you agree that Get Out, Her, The Martian, Joy, Birdman, and Silver Linings Playbook are all comedies/musicals, then Golden Globe categories don't mean much.
