Be ecstatic with the curiosity and self-learning. Those are the skills that have served me well in life. Having a wide range of interests and never being a master in one is fine. The ability to teach herself a wide range of topics will open many doors.
More to the point, I believe the ability to foster connections between a wide variety of topics & ways of knowing will open many doors. Singular focus is not the unique path to success, aggregating knowledge and wielding it coherently (even if tenuously) is also quite potent.
Consider every stereotypical intellectual TED talk you've seen, chances are it either goes deep on one idea or develops its uniqueness by combining ideas that create a new adjacency.
Granted the "jack of all trades, master of none" phenomenon is real but it's still predicated on mastery of singular topics being the target. Breadth combined with sufficient depth to be dangerous, as well as the ability to communicate clearly, enables people to organize and align disparate ideas that people can rally behind. Every skilled product manager, marketer, and executive needs to be able to cross over from their core expertise, and general curiosity and the ability to dive into many things at once is fundamental to those sorts of successes.
