Ukraine began its involvement in the Iraq War on 5 June 2003, shortly after the 2003 invasion of Iraq. As part of the Multi-National Force – Iraq, they engaged in combat with Iraqi insurgents. On 9 December 2008, Ukraine formally withdrew its last forces from Iraq, ending its participation in the Iraq War. Prior to the Russo-Ukrainian War, Ukraine’s involvement in the Iraq War was the largest military operation ever performed by the Armed Forces of Ukraine. Over 6,000 Ukrainians performed military service in Iraq and Kuwait during the war, including a permanent presence of 1,600, with more than 40 Ukrainians wounded and 18 killed in action.
It is my understanding that the newly formed Russian Federation assumed the debts and obligations of the Soviet Union. For example, Russia has the USSR’s UN Security Council seat. In the case of these missiles, IIRC, they were operated by the Soviet SSR missile corps. Ukraine at the time had no ability to operate or maintain this stockpile.
More in-depth info about these various myths: https://cisac.fsi.stanford.edu/news/budapest-memorandum-myths