If you go to the web app on the in-game phone, there's a whole bunch of explanations on the different systems. Basically the stars are the times you successfully gifted and hungout with them, you'd need 3 of them (successfully gift and hangout 3 times) PLUS the heart icon to advance the story.
You could always leave a donation on itchio or simply by following the progression of the game, rating it 5 stars, and sharing it with people who also like playing these types of games
