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PostMessage now rejects a chat sent on a finished game or when it is not the sender's turn (ErrChatNotYourTurn -> 409 chat_not_your_turn), matching the UI where the message field is hidden off-turn and only the nudge shows. Existing chat tests post on the to-move seat and are unaffected; adds an off-turn-rejection integration test + the dto mapping case + the UI error message.