Some of the new soundtracks can play in the normal biomes when playing on survival or creative, but nothing was mentioned about these tracks playing in normal biome, instead they were intented to play only in the new biomes or the title screen.

/playsound minecraft:music.game music @a ~ ~ ~

/playsound minecraft:music.creative music @a ~ ~ ~

These are the tracks that can be heard:

• Left to Bloom
• An Ordinary Day
• Floating Dream
• Comforting Memories

Maybe a few others too but generally, you can still hear these music tracks outside the places they're intended to play.