How can I copy the new camera view (after user drag)?

The position, direction and up should be sufficient to capture the camera view. This is my go to snippet for saving camera views: How to share custom Sandcastle examples.

Instead of viewer.camera.flyTo you can also use viewer.camera.setView like in this example: https://sandcastle.cesium.com/index.html?src=3D%20Tiles%20Feature%20Picking.html

// Set the initial camera view to look at Manhattan
var initialPosition = Cesium.Cartesian3.fromDegrees(
  -74.01881302800248,
  40.69114333714821,
  753
);
var initialOrientation = new Cesium.HeadingPitchRoll.fromDegrees(
  21.27879878293835,
  -21.34390550872461,
  0.0716951918898415
);
viewer.scene.camera.setView({
  destination: initialPosition,
  orientation: initialOrientation,
  endTransform: Cesium.Matrix4.IDENTITY,
});