This is Utriusque Cosmi by Robert Charles Wilson.

You can read the full story online here, courtesy of Clarkesworld Magazine.

Humanity is offered a choice;

“The world won’t last much longer,” Erasmus said in a low and mournful voice. “You can stay here, or you can come with me. But choose quick, Carlotta, because the mantle’s come unstable and the continents are starting to slip.”

and gets uploaded into a sort of galactic consciousness;

The plain wasn’t “real,” of course, not the way I was accustomed to things being real. It was a virtual place, and all of us were wearing virtual bodies, though we didn’t understand that fact immediately. We kept on being what we expected ourselves to be—we even wore the clothes we’d worn when we were raptured up. I remember looking down at the pair of greasy second-hand Reeboks I’d found at the Commanche Drop Goodwill store, thinking: in Heaven? Really?

The protagonist uses slow-time ("saccading") to survive well beyond the rest of the human race;

Apparently, it wasn’t necessary to “exist” continuously from one moment to the next. You could ask the Fleet to turn you off for a day or a week, then turn you on again. Any moment of active perception was called a saccade, and you could space your saccades as far apart as you liked. Want to live a thousand years? Do it by living one second out of every million that passes. Of course, it wouldn’t feel like a thousand years, subjectively; but a thousand years would flow by before you aged much. That’s basically what the Elders were doing.

And there's an enemy gobbling up the universe;