She's been busy ever since last week.

Literal

She [topic-は] last-week [since-から] all-along busy.

ずっと means 'continuously' or 'all along,' emphasizing unbroken duration. Combined with から (since), it creates 'has been ~ ever since' — a pattern for expressing that a state has persisted without interruption from a specific starting point. This is one of the most common and useful temporal adverbs for learners to master.