Donald J. Trump and his political team spent nearly two years tailoring a campaign to defeat an old white male president who is conspicuously frail and who most Americans had told pollsters they doubted could handle another four-year term.

Suddenly, Mr. Trump faces a starkly different opponent: a vice president who is a Black woman, nearly 20 years younger, and who brings her own strengths and weaknesses but who adds new uncertainty into what had been a remarkably static race.

Allies of Ms. Harris have already telegraphed that she will run a campaign framed around a “prosecutor versus felon” theme, highlighting her experience as a prosecutor and underscoring the fact that Mr. Trump has been indicted in multiple jurisdictions and…