Good day. The App is really great, but I can't find a way to toggle "Only Show Favorites" on "Clipboard / Pasteboard History" by hotkey
You can't find it because it probably doesn't exist. 
But you can create your own macro (2 actions) and assign the shortcut you want.
- Move mouse to ... (on the star)
- left click (on the star)
This relative to the upper left corner of the active window, which is the window you have in your post.
PS: Ah, sorry, no. BTT doesn't seem to recognize this window. So you can't move it. Use image recognition. Because unfortunately the icon changes, it needs a cycle action that recognizes both icons. But this works. 
Thank you for this idea. As I use the Paste window on half of the screen star button is always on the same place, so it is enough for me just move pointer to this coordinates and emulate click.
In the current versions you can use opt+cmd+F to toggle the mode
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Thank you. By the way I used the same combination for my own macro 