WWII showed the world that battleships were helpless against naval air superiority.
I would say that causality is backwards. Radar existed in the 1930s but was never seriously developed. But imagine a world where it had been and that battleships had radar-directed AA guns, perfectly do-able in the 1940s. It would very early on in WW2 have been "proven" that aircraft couldn't touch a battleship at sea and so noone would have bothered to invent carriers. Air superiority became a thing because battleships were helpless against it, not the other way round.
Radar directed AA guns were totally a thing in the 1940s. The US developed the Mk37 director (using the Mk4 radar), and had it in service before Pearl Harbor.
Carriers were invented well before this. And would have been invented regardless, as they were useful for more than just sinking battleships. The fact that they could sink battleships resulted in them becoming the preeminent surface combatant.
But carriers were useful for scouting, for land attack, for defense against enemy aircraft, for anti-submarine warfare, for killing smaller surface combatants (like destroyers).
I would say that causality is backwards. Radar existed in the 1930s but was never seriously developed. But imagine a world where it had been and that battleships had radar-directed AA guns, perfectly do-able in the 1940s. It would very early on in WW2 have been "proven" that aircraft couldn't touch a battleship at sea and so noone would have bothered to invent carriers. Air superiority became a thing because battleships were helpless against it, not the other way round.