It still seems as if the United States wants to withdraw completely from the region
It's unclear what you mean by that, but the US has regained interest in the ME, particularly when it comes to oil, not necessarily for itself, but for its European allies... which are facing the difficult problem of cutting those ties with Russia.
So, Biden is now on a tour that includes Saudi Arabia, although the US insists it's not going "hat in hand" for oil. The ceasefire in Yemen, agreed earlier this year gives the US a bit of cover to claim that indeed relations with the Saudi-led coalition are improving.
Regarding withdrawal from Iraq, I don't know if anything has changed, but the article you've linked to said:
President Joe Biden says US forces will end their combat mission in Iraq by the end of this year, but will continue to train and advise the Iraqi military. [...]
Numbers of US troops are likely to stay the same but the move is being seen as an attempt to help the Iraqi PM. [...]
Political parties aligned to Iran have demanded the withdrawal of all forces from the US-led global coalition against IS, despite the continuing threat posed by the Sunni jihadist group.
Which doesn't sound like a real withdrawal was planned. And according to Wikipedia (citing a Dec 9, 2021 Reuters article), that's what happened:
The U.S. formally concluded its combat mission in Iraq on 9 December 2021, leaving the 2,500 troops remaining in the country to serve as trainers and advisors to the Iraqi security forces.
As for Syria, you've linked to Trump's announcements from 2019. Those had already been implemented to a large extent before Biden came to office. I'm not sure what Biden's announced strategy is for Syria, if any was made public, but troops were still there in late 2021, and came under some attacks.
According to a Reuters article from this month:
The United States has roughly 900 troops in Syria, mostly in the east of the country splintered by a decade of civil war, although President Joe Biden's administration has yet to detail its long-term plan for the eight-year-old mission.