How a navy could regenerate carrier air power in World War III

Would STOVL be the only practical way to regenerate naval air power quickly in a major war?

For the fastest emergency response, yes: existing STOVL aircraft and converted merchant hulls are the practical route, while purpose-built CATOBAR replacements take much longer.

Existing F-35Bs could operate from rapidly adapted merchant hulls, making STOVL the quickest way to replace lost flight decks if suitable aircraft are already available. Replacing an air wing is a different problem from replacing its carrier, and the relatively small number of aircraft in a carrier wing offers some scope for regeneration. Merchant conversion avoids the years needed to build a new carrier. Bulk carriers are proposed as better conversion candidates than oil tankers because their holds are easier to clean and adapt into hangar-like spaces. Their flat decks also provide a useful starting point for flight operations. This is an emergency answer whose usefulness depends on aircraft stocks and the time available.