You can use the Envelope deformation effect, but you need to convert to path each object, because the Envelope deformation tools works only on paths or group of paths.
In the following example I've converted to path rectangles, circles and text just by grouping all the objects and using Path...Object to path. With the group selected, you need to show the Path effects dialog (Path...Path effects or Ctrl+Shift+7):
Clicking the "+" button, you can add the Envelope deformation effect:
Now you need to perform some manual work. The effect allows to apply a deformation to each side of your object.
You can start with the top side, by clicking the related Edit on-canvas icon:
Dragging the nodes you can see immediately the deformation, e.g.:
And so on:
With a little tweaking you can achieve a result similar to the desired one.