Scharnhorst shows what a real light battleship looked like

What would a proper pocket battleship that genuinely worried Britain look like?

Much like the Scharnhorst class: a light battleship with the protection and speed to be a serious raider.

The Scharnhorst class qualifies as a light battleship because its armor, hull, and intended role are battleship-like even though its available guns were only 11 inches. Those guns reflected what German industry could provide when the ships were built, rather than a battlecruiser design philosophy. Gun caliber alone cannot change the underlying type, just as a later 15-inch rearmament would not suddenly transform the hull into a battleship. Combining diesel cruising with steam-turbine speed would make such a raider more dangerous by extending its range.