Furthermore, economic growth is measured in "real" dollars, aka, excludig inflation. If US prices doubled as you say, then their economy is therefore now four times as large in the new, inflated dollars.
None of this has anything to do with fiat currency. The same would be true if you measured in kg's of gold, but you'd have to account for the gold-cost of living ratio instead of fiat dollar inflation.
Using the World Bank's figures in 2015-dollars https://data.worldbank.org/indicator/NY.GDP.MKTP.KD?location...
GDP 2008 US: 16.38T EU: 13.19T US/EU: 1.24
GDP 2022 US: 20.95T EU: 15.21T US/EU: 1.38 (2023 not yet available)
Ratio of ratios: 1.11, so the US has increased its lead by about 11%, which is not nothing, but also less dramatic than it looks to me in the "current prices" chart.
Sometimes lying with numbers is way, way to easy...