The war against Iran inside Iraq rages at a low level:
Iraq has slipped into an unofficial civil war between pro and anti-Iran factions. Iran has used force against anti-Iran protesters, responsible for most of the 550 protesters killed since the protests began in October 2019. These deaths have exceeded the casualties caused by Islamic terrorists. Half the deaths have been in Baghdad and Iraqis know Iran is a big fan of shooting protesters. In the same time period over a thousand protesters in Iran were killed.
Sadr continues to maneuver between the pro- and anti-Iran factions, with his ambitions the only constant:
Sadr ordered his armed supporters to use force to suppress anti-government protestors. The reaction to that was much more anti-Sadr than Sadr had expected. Suddenly he was tagged as just another opportunistic, pro-Iran Iraqi leaders. Sadr had guessed and wrong and, even though he remained hostile to Iranian influence in Iraq, he was an opportunistic Iraqi politicians who was willing to kill Iraqi Shia if he thought it would increase his power.
And in the broader war, Iran is on shaky ground since America killed terror-master Soleimani:
Soleimani was supposed to win some spectacular victories against Israel and America and thus justify all the band behavior by Iranian religious leaders/rulers. With the loss of Soleimani the Iranian leaderships is even more desperate and likely to do something spectacularly stupid and destructive.
I've warned that Iran could lash out militarily under economic pressure from America.
And I'm definitely a long-time worrier about three-time insurrectionist Sadr.
As for the battle with Iran over the fate of Iraq, I've been talking about this since the destruction of the ISIL caliphate in Iraq, and call it Phase IX of the Iraq War begun in 2003 (and that assumes we call the gap between the 1991 Persian Gulf War and 2003 as "peace" rather than a low-level war against Saddam's Iraq). I don't know what the defining main effort in this phase will be.
Keep an eye on Iran. They might try anything to reverse what they might see as their gathering defeat.
UPDATE: I suppose this rocket attack could be ISIL but I'd bet on Iranian-backed or controlled forces:
Multiple rockets hit an Iraqi base hosting American troops near the US embassy early Sunday, the latest in a flurry of attacks against US assets in the country.
"The Coalition confirms small rockets impacted the Iraqi base hosting (coalition) troops in the International Zone... No casualties," said coalition spokesman Myles Caggins.
The battle rages.