Minecraft wiki entry for Crimson_Forest, associated text: When the crimson forest was announced at MINECON Live 2019, which happened before the first Nether Update snapshot was released, it was known as "Nether wart forest". In the announcement, however, it was called "Nether wart forest red".
Most of the ambience in the crimson forest was made with balloons, which Samuel Åberg says creates a disturbing feeling of something stretching and forcing itself to bend.[1]
This biome might be a reference to a biome in the game Terraria, in which there is also a red biome called the Crimson. There is also a similar ocurrance with the blue Hallow biome and the Warped Forest.
The music track titled "Chrysopoeia" is a reference to the real life term Chrysopoeia, a term in alchemy referring to the artificial production of gold. This further ties the Nether to both brewing and gold.