There are some aproaches, but my favorite is to keep all that on vectors.
For the shadow duplicate your object, asign it diferent colors (preferible transparencies) and use the blend tool.
You can put over the original object.
With this method you can control the direction, longitude and intensity of the shadow.
The tradeoff is that you, in some cases, need to export at a higher resolution and resample, becouse there is a chance, depending on your settngs, that the steps are visible. (in my image they are if you zoom in)
However, you can make some aditional steps, like duplicating that "shadow" (keep the original) convert it to bitmap and blur it a bit. You can use directional blur.
If needed you can put that inside Two Power Clip (one for the interior and one for the exterior), becouse the blur can ocurr in both directions, spilling some shadow on the wrong side.
You mention one thing... "As soft"
If you knew how to do this, but the shadow is pixelated, either increase the resolution of the effects, or work at a bigger scale and resample after.