Basically, in the US, we are in a recession when the Business Cycle Dating Committee says so.
This would be the same regardless of which party were in power, the government lies.
"What is a recession? While some maintain that two consecutive quarters of falling real GDP constitute a recession, that is neither the official definition nor the way economists evaluate the state of the business cycle. Instead, both official determinations of recessions and economists’ assessment of economic activity are based on a holistic look at the data—including the labor market, consumer and business spending, industrial production, and incomes.
"[...] The National Bureau of Economic Research (NBER) Business Cycle Dating Committee—the official recession scorekeeper—defines a recession as “a significant decline in economic activity that is spread across the economy and that lasts more than a few months.”"
You can certainly make the argument that people shouldn't use this definition or that better measures exist, but it's objectively the official definition used by the US federal government.
[1] https://www.whitehouse.gov/cea/written-materials/2022/07/21/...
Here's the thing -- there is no "official" or "legal" definition of recession in the United States. Yes, you'll hear regulators and politicians defer to NBER, but that's it.
The most common definition used by economists and the financial industry is the same one used world-wide: two quarters of negative growth. And by that measure we're in a recession.