Therefore I should infer that only 1 full game turn is played per chapter - and so the introductory scenario The Letter is supposed to be played entirely in a single game turn?
yes. that's how we read the rules as well.
In these 24 hours (12 actions) you have to investigate all 1. chapter plot cards.
Planning phase: so flip as many as needed to find them all. turn more if you want to. and plan your actions. Story phase: let the action happen.
then - Endgame.