Right now, for me, this button is only displaying in the Beta and Nightly versions. It does not display in the Release version. I have the sidebar disabled at brave://settings/appearance and I too think this button should not display if that setting is disabled. I do not know if this is a bug or if Brave intends to keep displaying this button even if the sidebar is disabled in settings. My opinion/preference: if the sidebar is disabled, this button should not display. The button should only display if the feature is enabled (mouseover or always options) in settings.
Saying that, I do like the button and actually like that you can pull up the sidebar by clicking the button without having to enable mouseover or always options. I do not like either of those options but I do like the button. However, I think this should be added as an option in settings and not as a permanent icon. So, instead of just 3 options, you would have 4: mouseover, always, button only, never. If never is selected, the button would not display.
I have it disabled as well, so that’s why I don’t understand why it’s still giving me the option in the toolbar. I’m using the beta version, so hopefully this won’t be something that is permanent, it’s pretty annoying.