Right now the scaffold uses the linear value of the animation controller, which results in a rather abrupt linear animation:

In the Material Design samples, you can clearly see that the bottom sheets are animated smoothly: https://material.io/design/components/sheets-bottom.html#behavior

The problem is that the animation controller is also to apply the movement caused by dragging the finger, which requires linear interpolation.