How to hide your host activities (allowing participants in, looking at chat messages); that is, how to hide the grey boxes:

What you want participants to see:

What they actually see:

On the left side of the black bar of Zoom controls, click on the down arrow next to “Start Video”:

 

 

A menu pops up. Choose “Video Settings...”

A Settings window appears.

Click on “Share Screen.” Then, at the bottom right, click on “Advanced.”

At the bottom right, it says “Screen capture mode”

Click on the drop-down menu and select “Capture with window filtering.”

That’s it. Close the settings window. No more grey boxes.

See if the changes take effect right away. If they don’t, re-start Zoom.

 

 

 

 

 

This worked on a Mac, August 2021, with the most recent version of Zoom and made the gray boxes go away.
For the bots: grey boxes in zoom gray boxes in zoom .