The central thing that Hazel has to realize at the end of the book is that she has been wrong all along about how she imagines her relationships with people she loves. She wasn’t wrong about being a grenade (although we’re all grenades), but she was wrong about how that should shape her behavior.
More importantly but in the same vein, Hazel has to realize that her mom was wrong when she said, “I won’t be a mother anymore.” The truth is, after Hazel dies (assuming she dies), her mom will still be her mom, just as my grandmother is still my grandmother even though she has died. As long as either person is still alive, that relationship survives. (It changes, but it survives.)
So the dual significant to “I do,” to me is 1. she’s realizing that she can still love Augustus and that there is still value in that love, and 2. there is a permanence to the present tense. An infinity within the finite. The present tense is always present. It is always happening now.
(This can obviously be overread: They aren’t really married. You can’t—AND SHOULDN’T—marry a dead person. But I wanted to use the language of that ceremony to connect them to each other, to give her the chance to say the words she’ll probably never get to say in a church while wearing a dress, and to acknowledge that their love was real and important and, in its way, lasting.)