Let's take a look at what supposedly happened when miracles were allegedly working before. Yeah, let's use the Bible as evidence.
Note: As a person born in a Roman Catholic environment, I can only speak for what happens in the Bible my parents gave to me. But I'm pretty sure this applies equally to any myth.
In the Bible, miracles shape things. I mean. Political leaders are nothing. Take the Plagues of Egypt: the most powerful country can be on its knees in a matter of days.
Basically, what was before dependent on masses or big administrations may now depend on the whims of a passing-by spirit or the will of a few organized miracle-doers.
What would happen? Pretty much anything you want. I mean, you haven't given any limitations to miracles. So I'm assuming everybody has a nuclear bomb in one hand and a "resurrection bomb" in the other. Everyone may die and come back, those that come on top would be those that manage to make themselves unattainable while maintaining a maximum chaos between other factions.
As a side note, governments would probably be overwhelmed way sooner that your time line expects. I mean, people coming back to life is not something the government would not notice. Governments tend to keep track on who is alive or dead on their land. Same for just healing. And that is just the immediate good stuff that may happen. A few high magnitude earthquakes or a permanent hurricane season could not be contained for 40 years.
Now, I'm gonna assume from your previous question that religion as taken a bit of growth from the phenomenon. We now have a motor for stability, with the actual capacity to do stuff (you did not precise whether religious people could do more than non-religious people, but that seemed implied in your questions).
My guess is, political leader are going to give a lot of power to their favorite church. I mean, if they are the most prepared for what the world is, why not handle things in a medieval style, with a religion-approved leader? Things seem to have taken a medieval turn anyway.
And, from my (restricted) historical perspective, I bet almost no religious leader would refuse to take power.