There’s an archetype of game called Princess Makers.

tvtropes.org/pmwiki/pmwiki.php/…/PrincessMaker

They’re easy to make, actually, all flags and variables, but it seems like a natural fit for what you want to do. The “princess” is usually pretty limited by the trainer, which can be herself or the dragon in this case. Have the dragon own a library and some something she can use for training and the game becomes about your princess getting Prison Jacked while finding ways to communicate with her rescue, with events and endings responding to the training choices.