I do not think this means what some news writers think it means. In a Wall Street Journal article, the news writer used the term this way:

A budget deficit contributes…by injecting more demand into the economy via spending than it subtracts via taxes.
…
But deliberately shrinking the budget deficit, via fiscal austerity, or expanding it, via fiscal stimulus….

What he’s talking about here is reducing government spending as austerity. Government spending is one component of the overall spending that is the demand component of GDP; the other component of demand at the GDP level is consumption spending by us citizens. But reducing government spending, while reducing that overall component of demand, isn’t austerity. That reduction simply reduces the level of competition between government on the one hand and us citizens and our private enterprises on the other hand for the same goods and services. That reduction in the government’s side of that competition at the very least reduces upward pressure on the price we citizens and our businesses face for those same goods and services, even eliminates pricing pressure in some areas, and in some few areas, allows prices to fall.

That’s not austerity, that’s an early step in prosperity.

The news writer again misused the term:

Fiscal austerity does the job with much less collateral damage than tariffs. Inflation goes down instead of up. Trading partners don’t retaliate. There’s no special-interest lobbying or corrosive uncertainty over who gets hit with tariffs for how long.
Austerity’s main drawback is that it slows growth.

Reducing government spending isn’t the only path to private prosperity, and done by itself can be decidedly reductive of that. Taxes directly take money away from both us citizens and our private enterprises. Some taxation is necessary for our government to do the things we hire it to do—pay our national debt, see to a defense capability adequate to the threats we face, and satisfy our nation’s general welfare in the ways delineated in our Constitution. Leaving taxes alone—or raising them—whether in isolation or in order to fund spending unrelated to those three purposes takes money away from us and our businesses that we’re better situated to allocate to our actual needs and wants.

Those taxes are the source of austerity inflicted on us by government. Reducing those taxes to the more minimal level needed to satisfy those three Constitutional requirements reduces austerity far more directly than reducing spending: every dollar left in our and our businesses’ pocketbooks and not taken by government is a dollar we can allocate more efficiently than government is capable of doing.

Reducing government spending—the news writer’s definition of austerity—actually indirectly facilitates prosperity if not actually increases it, and reducing taxation—not addressed at all by the news writer—directly increases prosperity by reducing real austerity, the taking of money from private coffers and putting it in government coffers. Doing both in concert with each other—that’s the far opposite of austerity.