CYCLES
How does shadow catcher work?
Add an object (cube)
Add a plane (big enough) under the cube
check the checkbox "shadow catcher" for the plane
add an HDRI
result:
UPDATE
Unfortunately you did not File->External data-> Pack Resources so all i saw was pink :(
But...i inserted my own HDRI, deleted your two materials you gave the shadow catcher (just delete all and add the default one) and then i got: