In the new version the labs all play at the same time and are not in sync. Are they supposed to play independently like in 1.0?

No changes to how it was implemented were made (like ever, I even forgor to update folder name this time, lol).
You might've been using mods below in previous versions of the game to sync up sounds of factory machines. They are not updated to 2.0 version of the game yet, so you totally should go and poke mod author to do it!
https://mods.factorio.com/mod/factorio-sync-sound-manager
https://mods.factorio.com/mod/factorio-synced-labs-sound

Another solution was posted in thread https://mods.factorio.com/mod/LabDansen/discussion/5f57d24e583b0dbdf3587194 by randomuser612, that you can implement yourself by editing sound.lua file in archive. I've never made this change to the mod, as it removes ability for labs to become louder in larger quantities.

I updated the mod :) but I'm not sure how much can be broken there, you're welcome