There is no [Rotate] icon on the Home screen or booklists because the devices which officially support rotation (e.g. Libra, Sage etc) only support it in an open book. There isn't a way to rotate Home or booklists.
On a not-officially-supported-rotation device like the Clara2E, with the old rotation hack you're using, you should see the icon correctly in an open book, but not on Home or booklists. On these devices the hack will still rotate Home and booklists by pressing the "invisible" icon location. Rotated Home screen looks pretty awful. I think maybe Kobo did have a plan to support landscape everywhere at one time but later decided not to bother. I suspect trying to get all the Home/booklist widgets laid out neatly for all of the Kobo screen-sizes in both portrait and landscape proved very difficult, especially when you also add the beta "Large Print Mode" option into the equation. Whichever Kobo developer was tasked with trying to perfect that feature probably has no hair left.
The "ghost" icon you're seeing may be exactly that - the ghost of the icon which displayed correctly in an open book on a not-fully-refreshed Home screen.