Why the G3 remained a battlecruiser

Were the G3s really fast battleships rather than battlecruisers?

No. Their design intent, armor coverage, subdivision, speed, and relationship to the N3 place them on the battlecruiser side of the contemporary spectrum.

Capital ships sat on a moving technological spectrum: a fifth-generation battlecruiser should outperform much older battleships. Armor coverage, subdivision, intended role, and contemporary classification matter alongside headline thickness, speed, and armament figures. A thick belt or deck over a small vital area does not provide the same protection as thinner armor covering more of the hull. The N3's greater protection and 18-inch battery provide the relevant same-generation comparison, while the G3 remained the distant-station battlecruiser element.