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.
I can confirm using /playsound minecraft:music.game music @a. The music affected is: comforting_memories.ogg, floating_dream.ogg, left_to_bloom.ogg, one_more_day.ogg. I couldn't confirm an_ordinary_day.ogg.