How does inflation correlate with more savings vs more spendings? - eviltoast

A recent article: https://www.stuff.co.nz/business/money/301022706/prepare-to-find-another-70-a-week-to-get-by-in-2024-asb

says: ..if households decided the worst was over and started to feel more confident about spending, it could push up inflation

But I thought it was the opposite;

More spending means more demand means more supply, which means production costs go down (due to economies of scale)… so inflation goes down?

But saving means less spending, means less demand, means less income for business, means costs go up… so inflation would rise?