Production of the dance sequences was actually quite a pain-staking process, as it was all choreographed and filmed in live-action format first, then animated over to match the cartoon environment that it's set in.
Mattel had originally wanted to make a series of Barbie princess animated films where Barbie plays a different princess each movie from a classic fairytale (Snow White, Cinderella, Aurora, etc.), but out of fear of copyright with Disney, these plans were abandoned. This is where this film materialized, as Disney had never adapted Swan Lake into a Disney Princess movie. It almost happened prior, when director Richard Rich pitched the idea to Walt Disney Studios in the 90's which was ultimately rejected. This resulted in The Swan Princess (1994), which was made from a collaboration between Rich and Sony Pictures, after he had left Disney.
In an attempt to heal the nation, on February 14, 2021, podcast hosts Richard Martin and Alexander "AJ" Jones of the Cult Popture Podcast released an 18+ hour comprehensive podcast reviewing the 37 Barbie films. The retrospective took over a month to prepare and features numerous guest speakers as well as an original song created specially for the podcast.