If a Tera Raid boss is badly poisoned (e.g. from Toxic), does the bad poison damage increase only after all 4 players have a turn or immediately after any player has a turn?
From experience, the Tera Raid Pokemon will only take damage from Poison or Burn at the end of their own turn. commented 9 hours ago by PhailRaptor
If Toxic hits a wild Tera Pokémon in a Tera Raid Battle, the Tera Pokémon is inflicted with normal poison, rather than bad poison.
As an aside, even if the Pokémon didn't purge debuffs or put up shields, due to the way Toxic works in raids (it does damage equivalent to 1/16+ of the base HP of the Pokémon, not 1/16+ of the raid HP, which is 25x of base HP), Toxic is fairly useless.
Source (Toxic DMG not increasing over time)
Toxic damage only takes effect after the Tera Raid Pokémon has made a turn. Toxic damage also doesn't gradually increase damage over time, it just does normal poison damage. Tera Raid Pokemon can also clear status, so it isn't very effective for getting damage off of the Pokémon.