The fight for Iraq continues:
Iranian efforts to dominate Iraq have fallen way short of expectations. For the moment Iran is still trying to halt Iraqi political or military decisions that weaken Iranian ability to do what they want in Iraq. This Iranian interference slowed down the formation of a new Iraqi government and continuing efforts to defeat the remaining Islamic terror groups in Iraq. Iran has political and military goals that clash with what most Iraqis want. Pro-Iran Iraqi politicians want to provide Iran with more access and influence over Iraqi government decisions. When it comes to the Iraqi security forces Iran wants its PMF units to maintain their independence from army control. That enables Iran to use Iraq for operations in Syria and against the Sunni states of Arabia (especially Saudi Arabia). Most Iraqis don’t want to be involved with the Iranian military goals in Syria (attacking Israel) or Arabia (fighting Saudi Arabia over oil and control of Islamic holy places.)
One thing that helps is that America and our allies remains in Iraq, unlike in 2011 when we withdrew our military and let jihadis and Iran gain strength.
A dangerous problem is that pro-Iran PMF (Popular Mobilization Forces, mostly Shia militias mobilized in 2014 after Iraqi security forces collapsed in the north) units in Anbar are causing problems for Sunni Arabs. The Sunni Arabs fueled the insurgency in the Iraq War until the Awakening; and they fueled the rise of ISIL. Iran would love to provoke the Sunni Arabs into revolt again to justify Iran's role in Iraq into the future.
In the surge offensive in the Iraq War, American and Iraqi forces took down the pro-Iran Shia militias in Sadr City and Basra. The creation of the PMF reversed that success.
One thing the American position in eastern Syria does is serve as a buffer to prevent the region from being used as a sanctuary for Sunni jihadis destabilizing Iraq as it was under Assad in the Iraq War and as it was as part of the Islamic State under ISIL.
On the bright side, the lengthy wars against jihadis has driven home an important point:
Opinion surveys show nearly all young Iraqis see no future in Islamic radicalism and terrorism, which has, for most of their young lives been more of a threat than a source of salvation. Down in Basra the ongoing riots and demonstrations are about basics, like clean water and regular electricity supplies. The Basra unrest has been going on since July (triggered by polluted drinking water) and at least 40 protestors have been killed and many more wounded or arrested. Dozens have disappeared and feared dead. The protestors note that Iran backed militias are also involved in attacking the demonstrators. This, for many young Iraqis, confirms suspicions that Iran is not their friend.
Iraq can yet stand as a beacon of democracy and, in time, rule of law in the heart of the Middle East. We want young Moslem men to see democracy and peace as the way to a better future rather than autocrats or mullah rulers who have screwed up the Middle East since the end of the colonial eras (under the Ottomans and then under Europeans) after World War II. South Korea was poorer than Arab states back then, remember.