I do a lot of car renders. The shadow really depends on your lighting, as in real life. A sunny day creates crispy shadows. Cloudy day soft and diffuse. I do struggle sometimes to get what I think Corona will create, and then have to resort to the old workaround. Once you have got it so the shadows are the softness you need, I set up two Takes.
Take 1 with the car and Alpha. Important to get the glass to be somewhat transparent. The regular mask usually just gives you the shape of the car with opaque windows. Compositing Tag to hide the background from camera. Set up a render setting to save as Beauty or something. It's important to have your image that is used in the comp to provide reflections and a ground effect, but not show in the render.
Take 2 is HIDE car from the camera. Replace the ground with a large plane that has a bright white material. Important that your object touches, or in the case of car tires, I always have them slightly through the "floor." Another render setting and save as Shadows. This can be a simple JPG still or sequence.
Then in your video software or image editor, have the background image and then drop the shadow render in with the car on top. Change the Blending mode for the white shadow layer to Multiply. Boom. You can now reduce opacity or play with levels or curves just on the shadow layer. You can add a blur as well. Don't go crazy though with blurs as you will mess up the contact shadows. Ambient Occlusion as it's called in the standard C4D render engine.
One limitation to my workaround is if you some type of bumpy floor/ground or something that breaks the shadow up, this method will not provide that level of detail.
Hope this makes sense. It works for me. I set up a simple scene showing this.
https://www.dropbox.com/scl/fi/i37nen5bx6lkt8lzvd166/Shadow-Workaround.zip?rlkey=e4t6qvsfy4tj8bk67g8qmaw56&dl=0
