I tested the settings. It looks much better now. Thank you!
Here are the recommendations we followed. Maybe somebody else will need them:
1) Go to your shadowcatcher material and make its backplate color darker - this will reduce global illumination in your scene and in turn will reduce overall noise.
2) Go to your shadowcatcher material and increase "shadow amount" value - I can see in your scene it is set to 0,1 and this additionally increases the brightness of GI. I suggest using value of 1 or more.
3) Do all lights in your scene need to have "shadowcatcher illuminator" option enabled? If this option is enabled in a light, not only shadows are included in the alpha channel generated by the shadowcatcher, but also the direct lighting coming from that light. This is useful, for example, if you are rendering a car in a garage, where the garage is a 2D backplate, and you want its headlights to cast light on the 2D backplate garage. But I am not 100% sure if this is needed in your case.
4) Go to Render Setup > Performance and increase GIvsAA balance value from the default 16 to 32 (but no any higher!) - this should make the noise resolve a bit faster at the cost of anti-aliasing quality.
We changed the background and added just a horizontal plane which covers the whole viewport as shadow catcher. This gives us now a new strange effect in the background which I don't understand...
Here a preview with the new introduces "black belt"