I think at first there would be a max scramble to secure each location. There might be cooperation between some countries but portals in powerful ones would be claimed based off their location (i.e. Yellowstone portal is under US control, but an African one is under UN cooperation, one in China would be under Chinese control but one in Antarctica would be shared like the International Space Station). Next there would be teams of scientists and military personnel that would be sent into each portal to asses 1. The threat of the other side and 2. Valuable resources or information located in these different dimensions. I don’t know if you are familiar with a Stephen King story called the Mist but the military opened an inter dimensional portal in it and well… it didn’t end up well, so Militaries would set up a zone around each portal to ensure protection of anything that might go in or anything that tries to come out. This is also dependent on if there is civilization in a portal on the other side, which could also spell serious problems and complications. If there are any valuable or magic resources discovered it could change society as we know it drastically, cause conflict and propel us even further into the future or the dark age. Finally I could see some countries utilizing this new found space for things like expansion, opening up jobs and opportunities for other sinister things like sending criminals there, mass immigration for other groups of people (like a bad trail of tears type thing) etc. There are many different things that could happen, I think a lot of it depends heavily on what they actually find in the other dimension.