I just wanted to point something out. So, recently, I’ve been attempting to use a shadow catcher with cycles on a transparent backdrop to display an item for print on white paper. However, when I do this, I get a highly noisy backdrop that is not apparent on the computer screen but is when printed. This is NOT the case when I use the LuxCore render engine. At first glance, this is not obvious. But then I increase the levels to the alpha channels, and this is what you see.
So, I tried your method, and it helped clean it up (a bit)…However, when I try to trim the image down too see how much of the background there actually is. It does not remove anything. To see what is going on, I increased the levels to 100%. And this is what you see.