What you are asking about, is usually referred to as the "turning circle", steering angle usually refers to the lean angle of the headstem. A steeper head angle will give you quicker steering, but a slacker head angle will give more high speed stability, it's a compromise between the two. Small scooters have a shorter wheelbase and smaller wheels, so they will always have a tighter turning circle.
If you look at your bike, with the bars fully turned to one side, you will probably see that the triple clamps or fork tubes are very close to the frame, and enough room needs to be left for electrical cables to run alongside the frame too. If the triple clamp or fork tubes are nearly touching the frame, then you won't be able to modify your bike to have a smaller turning circle.
One thing you can do to make slow, tight turns much easier, like for a u-turn or parking, is to lean the bike over to the inside, but keep your upper body 90 degrees to the ground, rather than leaning with the bike.