Given the geostrategic situation there, either the West or Iran meddles in Iraq. Full sovereignty is hard to achieve in such a neighbourhood unless you are one of the traditional powers (Iran, Turkey).
Nobody has full sovereignty. As long as Iraq can sell their own oil without routing through Langley or Tehran, then it's all good.
Looking at the Hormuz Strait, they'd better build a very good pipeline to the Mediterranean. Both the US and Iran seem to be very interested in controlling who sails through.
Iraq isn't interested in bombing Gaza or Lebanon so I don't foresee they will have issues. Iran and Iraq are more aligned than Usrael and Iran.