Baghdad says the remaining U.S.-led coalition forces are completing their withdrawal from Iraq, bringing a military presence dating back to the 2003 invasion to an end. The agreed final deadline is September 30.

For Iraq, this is a major sovereignty milestone: Iraqi forces now assume full responsibility for security, while foreign bases can no longer serve as permanent targets in the confrontation between Washington, Tehran and armed groups.

For Washington, meanwhile, military withdrawal does not mean the disappearance of American influence.

The clearest example is financial.

Much of Iraq’s oil revenue remains held through an account at the Federal Reserve Bank of New York. Oil finances roughly 90% of Iraq’s state budget, giving Washington significant leverage over Baghdad’s access to dollars. Reuters reported this year that U.S. officials threatened restrictions on those funds during disputes over Iran-aligned factions entering government; Washington also temporarily halted some dollar shipments earlier this year.

And the political influence is equally difficult to ignore: Washington openly opposed certain candidates during government formation and strongly backed Prime Minister Ali al-Zaidi, although his government ultimately received the constitutionally required approval of the Iraqi parliament.

So has America left Iraq?

Militarily, yes — its permanent troop presence is ending.

Strategically and economically, not entirely.

The next struggle over Iraqi sovereignty may therefore be less about foreign soldiers on Iraqi soil and more about who controls Iraq’s money, security relationships and political room for manoeuvre.