The only international organization the could manage something like that that would have a possibility of keeping a free and open internet would be something like the UN for world wide usage where a sub organization, with open books would need to be audited by anyone, see my other response in this comment chain for more details.

The way Starlink or any other satellite constellation works would be either destroyed in functionality by being removed from said constellation, they can only connect to a larger network or satellites for their functions to be useful, or the country’s control over a few of the total would be functionally useless. The best option in that veign would be for SpaceX or whatever company runs the constellation to be owned by all governments proportional to their population but that would have issues where countries like Russia, China, the US, NK, and Israel would then have more access to the constellations to spy on all people and censor everyone world wide more directly. I don’t think that would work it would make things worse most likely and would be completely unfeasible. I think a non profit something along the lines of the ACLU but world wide running it for the benefit of humanity with privacy, freedom of speech, and that sort of thing in their charter while being functionally immune from state/government interference while operating under those parameters would be the most feasible solution which would be ugly but maybe better, maybe with the UN as the overall backer of the constellation management, making it a more powerful entity but stopping the US, China, Russia, France, or the UK from individually controlling the way the constellation is used, and forcing all countries in the UN to allow access to the free and open internet.

There are a few problems with that, would it be owned by the UN with US, Russian, British, French and Chinese veto powers over its use? Would it just be one country, and then the US would be able to help let’s say Russia by turning down physical speed limits of internet connections for drones cutting out musk from the equation? Would it be based on whose airspace they are in at the time to rent out the data as required, thus stopping Ukraine from doing deep strikes into Russia? Also and most importantly figuring this out would be hard work and politicians are historically lazy on things that don’t affect them personally and why would they fight Elon musk to nationalize SpaceX or the satellites they own for Starlink when they can just sit back and be bribed much more easily?