Yes, the only listed combatant countries are fucking the US, UK, Poland, Australia, and allied Iraqi forces. Ive met enough fucking veterans to know who they fought with during the initial invasian from anecdotes alone and post invasion was the US, UK, and local forces.
Yes secondary assistance was given, but guess what only direct fucken involvement matters. Ill even qoute the fucking beginning of the fucking NATO article on the matter and the nice little list of NATO adjacent actions.
“The March 2003 campaign against Iraq was conducted by a coalition of forces from different countries, some of which were NATO member countries and some were not. NATO as an organisation had no role in the decision to undertake the campaign or to conduct it”
And heres the little list.
NATO as an organisation had no role in the 2003 campaign since opinions among members were divided, as they were in the United Nations.
Iraq was suspected of possessing weapons of mass destruction and was requested to comply with disarmament obligations.
The US-led coalition, operation Iraqi Freedom, ousted the Saddam Hussein regime.
Prior to the campaign and at the request of Turkey, NATO undertook precautionary defensive measures by deploying for instance surveillance aircraft and missile defenses on Turkish territory.
NATO also supported Poland - a participant in the US-led Multinational Stabilization Force set up after the campaign - with for instance communications and logistics.
The closest fucking thing to actually getting involved in Iraq is the logistical assistance during occupation and that was largely in poland and the UK.
Here the fucking article on the NATO website if ya want to look further. Most of it is dedicated to the thing with Turkey.