The matter is more complicated since there is another government in Yemen based in the southern part of the country which enjoys broad international legitimacy even though it controls neither the capital nor the armed forces
There are also further separatist forces in Aden which aspire to establish their own state of “South Arabia”
However there is no shortage of historical precedents for changes of government that earn legitimacy from international forums Afghanistan, for instance, is currently ruled by the Taliban following the hasty US withdrawal from the country in 2021