My simple understanding is that embassy ground is regarded as sovereign soil of the representative country, therefore it would be classed or viewed as a direct attack maybe along the lines of, “Sir, The United Sates of America is under attack…”
According to this Fox tweet at the time and assuming it is accurate (translation), the militia made an open declaration of their leaderships identity:
“Soleimani is our leader” written under window by Iran-backed militiamen at U.S. Embassy Baghdad, about head of IRGC’s Quds Force, responsible for special operations in Iraq and Syria
5:16 PM · Jan 2, 2020·Twitter for iPhone
Unsurprisingly, Israel wanted to take out Soleimani back in 2015, Obama Admin prevented this:
…The Trump administration, on the other hand, gave Israel a green light to assassinate Soleimani, according to a January 1, 2018 report from the Kuwaiti newspaper Al-Jarida . The paper quoted a source in Jerusalem as saying that “there is an American-Israeli agreement” that Soleimani is a “threat to the two countries’ interests in the region.” According to Haaretz , Al-Jarida is generally assumed to be a platform for the Israeli government to disseminate its message to other Middle Eastern governments.
According to the report, the agreement between Israel and the U.S. came three years after Washington thwarted an Israeli attempt to kill the Iranian general.
> “The report says Israel was ‘on the verge’ of assassinating Soleimani three years ago, near Damascus, but the United States warned the Iranian leadership of the plan, revealing that Israel was closely tracking the Iranian general,” Haaretz reported.
The incident “sparked a sharp disagreement between the Israeli and American security and intelligence apparatuses regarding the issue.” That sounds like an understatement.
President Barack Obama frequently snubbed Israel, considered by many to be America’s best ally in the Middle East. Yet the news that the Obama’s administration prevented Israel from assassinating the Quds Force leader seems particularly significant, since the Obama administration also kept a list of approximately 500 American soldiers who were murdered by Iranian IEDs. Since the Quds Force spearheads Iran’s operations outside the Islamic Republic, Soleimani would arguably be responsible for all of those deaths.
When Trump finally gave the order to kill the Quds Force leader, it came after multiple attacks against Americans and American facilities in Iraq — attacks that arguably traced back to Soleimani himself.
The Iran-backed Iraqi militia Kata’ib Hezbollah began the escalating tensions with a rocket attack on a U.S.-led coalition base on December 27. That attack killed a U.S. contractor and left many American and Iraqi personnel wounded. According to the Pentagon, Soleimani ordered that attack.
In response, America launched airstrikes against the militia, killing 25 militiamen. In retaliation, the militiamen stormed the U.S. Embassy in Baghdad, invading American soil. The Pentagon claimed that Soleimani “approved the attacks on the U.S. Embassy in Baghdad that took place this week.”
Killing Soleimani is a powerful response to the embassy attack, an attack that arguably constituted an act of war.
Report: Obama Administration Stopped Israel From Assassinating Soleimani in 2015 – PJ Media
The Obama admin appear to have be very favourable to Soleminai, as noted in the Telegraph article surrounding some of the terms of the Iranian deal:
Obama’s Iran deal has just granted an amnesty to the world’s leading terrorist mastermind
CON COUGHLIN JULY 15, 2015
Qassem Suleimani, the head of the elite Quds Force in Iran’s Revolutionary Guards, fully deserves his reputation as one of the world’s leading terrorist masterminds.
For a decade a more he has been the driving force behind an array of Iranian-sponsored terrorist groups, from Hizbollah to Hamas, which have orchestrated a reign of terror throughout the Middle East.
From a purely British perspective, he was responsible for training and equipping the Shia militias in southern Iraq who killed scores of British troops during the dark days of Iraq’s sectarian conflict following the overthrow of Saddam Hussein, and was reported to have trained the Taliban in the art of making deadly roadside bombs that killed and mutilated our Service personnel serving in southern Afghanistan.
So you can imagine my amazement when, leafing through the more obscure annexes of President Barack Obama’s “historic” deal with Iran (page 86 of the annex, to be precise), I found that Mr Suliemani – as the White House no doubt now refers to him – has been granted an amnesty and taken off the list of proscribed Iranians – together with a number of senior members of the Revolutionary Guards.
Thanks to Mr Obama’s scandalous capitulation to Tehran, Mr Suleimani has overnight gone from being one of the world’s most wanted terrorists to the White House’s newest best friend…
…If I were Suleimani, I’d be organising an enormous party right now to celebrate a deal that is truly a “historic victory” for Tehran.
Alternative Link to Article Text: https://outline.com/66dzsx
Read Full Article here: Obama's Iran deal has just granted an amnesty to the world's leading terrorist mastermind
In a follow on interview a few days later, this aspect of the deal is aired in a questioned to Kerry:
Interview With Chris Wallace of Fox News Sunday
John Kerry, Secretary of State
July 19, 2015
QUESTION: Under this deal, we lift the arms embargo on Iran being able to buy weapons and even ballistic missiles between five and eight years. And the sanctions against General Soleimani, head of the Iranian Revolutionary Guard’s Qods Force, are also lifted. What we end up with, Secretary Kerry, is an Iran with billions, hundreds of billions of dollars more, able to buy weapons, and a Revolutionary Guard with fewer restraints. Isn’t that potentially an even more dangerous state sponsor of terror in the Middle East?
SECRETARY KERRY: First of all, Chris, don’t exaggerate. It’s not hundreds of billions of dollars. It’s $100 billion…
Interview With Chris Wallace of Fox News Sunday