Your extension should specify an icon for the sidebar in the sidebar_action manifest key. This is called the "manifest icon".
If you don't specify an icon in the sidebar_action key, you get the browser's default icon. This is called the "default icon".
If you set a new icon using setIcon(), and include the tabId option, then the icon is set only for the given tab. This icon is called the "tab-specific icon".
If you set a new icon using setIcon(), and include the windowId option, then the icon is set only for the given window. This icon is called the "window-specific icon", and will appear in all tabs of that window that do not have a tab-specific icon set.
If you set a new icon using setIcon(), and omit both the tabId and windowId options, then this sets the "global icon". The global icon will then appear in all tabs that do not have a tab-specific icon set and whose window does not have a window-specific icon.