California added jobs faster than the rest of the nation over the past year. Tech firms are showering riches on Silicon Valley, and home prices are soaring in places like Palo Alto. The Golden State is rebounding, but for a broad swath of residents, it is a lot less golden and is likely to stay that way.

Even in Silicon Valley, many aren't joining the revival. Tech companies are thriving, but only after shifting much work elsewhere. Internet-software experts are in demand; middle-aged semiconductor executives aren't.

Among...