The Baker chains so long as the new Baker’s original role is not corrupted.
If not corrupted, the first Baker flipped (or Doppel baker) truthfully says “I am the original Baker”. It then targets a still facedown villager card to become a baker, who when flipped will try to baker another villager, creating a chain. The chain breaks if a baker tries to target a corrupted character, who will turn into a baker but lie about what their original role was and will not baker any more facedown cards.
A puppet who was a baker will claim “I was a baker.”
The strat in the game you just played would have been to shank the confessor, since there are no outcast disguisers to worry about (so bomby is real). If the confessor was corrupted because the poisoner was nearby (only 1 corruption in this game and they must be next to the poisoner), the poisoner must be the #5 baker claiming medium because 7 was telling the truth. And Baa would be the dreamer because demons can’t be the same role as a villager and the other bakers are clear.
Of course, shanking the confessor would have revealed Baa, meaning 7 was lying and you could validate the dreamer on Baa to reveal the dreamer was also lying. Then it becomes a fifty-fifty choice about who to shank (you still have 10 health, so you win).
Sometimes the best strategy is to figure out potential solutions and then spend the free kill on someone suspicious you think you would break the conundrum.
This is also why Baker games are tricky because the jester and medium might have given you more and better information.