We have bases still in Iraq, but we fucked up so bad there that major troop withdrawal was done at the end of 2011. Obama tried to keep our troops there longer, but the Iraqi government basically kicked us the fuck out, and we only had 500 soldiers there as of December 2011.

We still have a presence there, but based on cursory research, it's shared space, like Balad AFB which houses the Iraqi military's F-16 squadron as well as US personnel. Al Asad Air Base has US personnel from four divisions of the armed forces, and there are Danish soldiers stationed there as well, and it seems one of the main uses of the base is the continued training of Iraqi soldiers. There may be more in Iraq, but they are smaller and likely short-term use.

An amount of US soldiers were deployed all over the middle east starting in 2014 as a support role in the overarching war against the Islamic State (ISIL), but they had been brought in as a support network for Iraq defending itself from ISIL after ISIL made significant successes in Iraq in 2014. Seems like there's only about 2,500 US personnel in Iraq all told since the end of 2021, and that was from agreements Biden organized for a continued US presence with an advisory and training role for US soldiers.

I would say being involved to help stop an invasion into Iraq and helping their armed forces along with a coalition of other nations also in support capacities was materially different than the US invasion in 2003.