The closest we’ve come to losing a supercarrier from damage was the Forrestal during her 67 fire and Enterprise during her 69 one.
Both ships too damage equivilant to multiple large missile hits. And could have, in a real world combat situation, been back and operational with temporary repairs in a short amount of shipyard time.
The only thing out there that has a shot of taking out a carrier is a nuke. Pretty much a direct hit with a nuke, as bikini showed (even extrapolating up for bombs with much larger yields)
Popping off a nuke at a carrier, whether it sinks the carrier or not, Issa whole different ballgame. Chances are someone will quickly lose a major population center ...
One aircraft carrier at Bikini was the Saratoga. The ship survived the blast, but it was radioactively contaminated, with no hope of decontamination. Faced with that, She was scuttled.
Saratoga was our 4th US carrier (virtual) at Midway. She was coming from refit in California, and the knowledge that she was on the way with a complement of aircraft let Spruance be a bit braver than he would have been otherwise.