I have run other things before, recently started running DnD, last couple months. In my experience the only real difficulty is balancing combat encounters and players will not be mad if they dunk on you while you’re learning, it’s a power fantasy for them in that case. If you’re confident you can improvise then all you need is a strong grasp on who is involved in your story and the things they want, so you can have them react rationally to the party, as you already noticed. Assuming you know the rules at least well enough to make rulings as you go.

All this to say no need to buy a module if you’re confident. I’ve never run anything from a book in any system so I’m biased maybe.