I've heard both ways that battleships were still thought to rule supreme at the start of World War Two, and that people had already begun to realize the future of carriers at that point.

This was both true: different factions of naval establishment in all countries had different views as to the role of naval aviation vs battleships.

For the USN "carrier focus" was forced upon them by the sinking of "battleship row" at Pearl Harbor in December 1941. The Pacific carriers were intact and thus used as primary offensive weapon because there was no other choice.

Ironically, the IJN, who pioneered the concept of massed naval air power as decisive offensive weapons, -continued- to view battleships as the primary weapon even after Pearl Harbor. Carrier air-power were suppose to weaken the enemy who will then be engaged by surface forces. It was only after the disaster at Midway that the Japanese Navy re-evaluated its doctrine and placed its remaining carriers at the center of its strategy, while using battleships as supporting weapons.