Why a naval Typhoon would be an entirely new aircraft

Would a larger British carrier lead to a navalized Eurofighter Typhoon?

No. Carrier suitability would require a comprehensive redesign funded largely by Britain, making Super Hornet the cheaper path.

Navalization is not a matter of fitting an arrestor hook: carrier landings are controlled crashes that impose loads throughout the aircraft. The airframe, landing gear, avionics, and internal structure would all require redesign, effectively creating a new type. France would pursue its own naval Rafale, while Germany and the other Eurofighter partners had no carrier requirement. Britain would therefore bear most of the cost even if carrier suitability were designed into the project earlier. Joining the Super Hornet development program is more plausible and fits Britain's practice of balancing European and American systems. The same aircraft could then serve the Fleet Air Arm and complement Typhoon in the RAF.