Set a custom icon

Based on this post and the documentation icon myicon.png has been loaded to /config/www. I ckecked that https://myip/local/micon.png works. Then in configuration.yaml has been added:

      entity_picture: /local/myicon.png

I noticed that myicon is displayed in the dropdown menu when selecting an entity but it does not show up in the button.

Am I missing something? Is it supported for the input_button?
Ultimately, I’d like to change the icon based on a certain state. Can I achieve that?

Thank you