US GDP is 30 trillion and government spending is 10 trillion, so does that mean real wealth is 20 trillion ?

The United States produces 20 trillion in wealth. HOWEVER, the government, through taxes, takes 10 trillion and distributes it to other areas (such as health, education, etc.)

I know that government spending is part of the GDP. But, if the government spends, someone is not buying, taxes are being collected.

So, government spending is not real wealth but distribution of wealth? Because if the government collected 20 trillion in taxes, wealth would fall to 0 and the GDP would be 20 trillion.