Why a large armored cruiser needs no new category

Is the large armored cruiser a separate step between the armored cruiser and the battlecruiser?

No. It is better treated as the upper end of the armored-cruiser range, especially a continuation of the first-class armored cruiser.

A larger hull does not require another classification between armored cruisers and battlecruisers. Armored cruisers historically ranged across first-, second-, and third-class roles. A particularly large example remains a continuation of the first-class armored cruiser. This keeps the distinction between cruisers and battlecruisers without inventing a redundant intermediate type.