How G3 and N3 would raise German battleship calibers

Would Germany need guns larger than 15 inches in a world where G3 and N3 entered service?

Yes; after an interim constrained design, Germany would be pushed toward much larger capital-ship guns.

Germany would probably retain the 11-inch Scharnhorst-class ships because that caliber was the immediate limit of its industrial infrastructure. British capital ships with 16.5-inch and 18-inch guns would then set a much higher standard for the next German design. A 15-inch battery would offer too little against those opponents. Germany would be pushed toward 16-inch or 16.5-inch weapons and might attempt 17-inch or 18-inch guns.