I think you're talking specifically about being the world's sole military superpower. That isn't what I think about when I hear "American exceptionalism", though it is part of it.
For people under 20, they've never lived a world where the US wasn't locked in a War on Terror, even though the most terrorists they've ever seen attack the US have been other Americans. Our sole super-power-ness has been of little value.
For people my age, we remember the brief period after the Cold War and before the War on Terror. We remember it fondly, but it's becoming dim. We crushed Iraq and Afghanistan but aren't thought of as victors.
We're #1 in military strength and will remain #1, but it doesn't matter. Maybe China will force us into the Thucydides Trap but they seem to prefer fighting economically. They like the saber-rattling, but then, so do we. I think we're all feeling a return to Mutually Assured Destruction dread, but it's not yet the top of our minds.
Closer to the top of our minds is all the other things I associate with American exceptionalism, and those are looking even more worn. There's a lot of current events poking at that, but even before pandemic and chip shortage, we were looking at a continuing stimulus for a recession that technically ended a decade ago, and a student loan crisis, and a generation that feels like it won't ever get ahead. We know we're still richer than poor countries but it doesn't feel like we're exceptionally, permanently superior.
And for those older than me, it looks to us as if they're wedded to the Cold World Order. They fight tooth and nail to praise the virtues of their childhoods, and declare that if America isn't exceptional it's because everybody younger than them has thrown off their own specialness. We're lazy, dumb, immoral, etc. That's just the usual generational grumbling, but ratched up to 11 by American Exceptionalism and a world catching up to us.
To those people, "American Exceptionalism" equates to "America is Number 1".
When America becomes "Number 2" in the near future, it would be an unimaginable disaster for those people. That's why the Wolfowitz Doctrine and the Thucydides Trap will bring actual disaster for the US - wars, financial collapse, etc.
Of course, those of us that are older can remember lots of times when America was not Number 1 at all. And so we're not as fussed about the coming demotions.