I see two big things that others have touched on. One, you wll not believe how much of a difference a real road bike makes in your speed once you have a chance to try one, and the average speeds you're seeing are almost definitely on road bikes. I don't think you need to go out and get one now or anything, get comfortable with what you have first, but also know that if/when you try one your average speed will probably jump at least 5km/h.

Second, cycling takes a lot of time to get used to. Anecdotally, when I first started I was a competitive distance runner and would occasionally win smaller races, and I started riding with a bunch of older relatively out of shape guys who had been cycling for decades. On about one sprint or hill a ride I could beat them, but they would kick my butt on the rest of the ride for more than a year before my conditioning caught up and I started to be able to keep up consistently.