Hi there! Saves from the Transcendent Edition will very likely not work with the full game (regardless of whether bought on Steam or Itch)
The Prologue is standalone, to some extent. The story will pick up after the end of the Prologue, but the plan is to work in player feedback and improvements that will likely change the codebase and game-flow too much to use existing saves.
As for your extra content: the Aura background will be in your Wardrobe from the off, and the new Tasks (and wardrobe puzzesl/rewards) will kick in at the end of the main/free content (after the end screen).
Hope that all makes sense, and thanks for picking up the game. Looking forward to hearing all your feedback!