I'll probably get myself defrocked for this because what I'm offering is more an alternative to shadowing because it's so easy to achieve and is completely independent of Blender's lighting restrictions, quirks etc.
The method is kindergarten level, crude even, but it works!
It's entirely flexible and has the added advantage of being able to
assume any shape a storyline demands. It can even move independently of its 'master', take on a life of its own!
The system uses a 2D alpha layered plane textured with the shadow movie or a still frame when no animation is involved. This is laid at the actor's or object's 'feet' and parented to the same empty that's propelling it forward. (for stability)
It can just as easily be placed on a wall, or bent half between!
Shadow movies can be blurred in the VSE when a sharply defined version isn't desirable, the plane textured with that instead.
They are also rendered using OpenGL and with no lighting. (Black on transparent)
A shadow is photographed/filmed as with any movie, capturing the actor's movements, but holding it (the actor) stationary. I find it easier to either duplicate the Blend file and do the shadow in that, or create a new scene and copy paste (append) the actor into it, animation and all. In the shadow Blend file all lighting is removed so you end up with a black figure doing its thing on an alpha layered background.
The examples above were rendered using OpenGL as png files, one for each frame and with the "RGBA" button pressed for the alpha layer.
I'd recommend setting up a fixed camera for this. It will give you somewhere stable to come back to, should the need arise.
The cam is usually placed at a position that gives the best results for the job. This isn't necessarily from where the scenario's lighting originates.
More often it can be at its 'compass' direction only, and at a height and angle to suit. In the Plant example, the shadow sequence was taken from about mid plant height and perpendicular to them.
The walking sequence was taken from directly behind and with the forward motion disabled. i.e. animated but stationary. Whatever 'stretching' is needed for the shadow's projection, is achieved by scaling the plane in that axis. Keyframes can rescale as necessary.
The craft taking off was just a still alpha layered 'photograph' to get its basic shape from the sun's angle. (It was not intended for this particular background photo)
The shadow plane was parented to the craft.
When the craft takes off and rotates, so too does the plane, so its Z height has to be held at its original setting. To add realism the width of the plane was scaled down with a keyframe or two to more accurately reflect the sun's projection angle.
Where more complex distortions might be required, shape keys can be called upon. (See the EDIT below)
EDIT 10th Aug 2022
EDIT 10th Aug 2022 -
Added a fourth clip above...
The last video shrink-wraps the shadow plane so it follows 'terrain'. (the hump in the floor)
It also encounters a wall and behaves accordingly. For that, a duplicate of the plane was added and placed vertically under the floor. It's ascent is tweaked to match 1st.