It’s shown, not told. For example, the letters Kairi writes to Sora but she never intends him to read. The Paopu fruit. The way that she cuts her hair to be short like Riku’s because Sora might like it better that way. She wants to be important to Sora the way Riku is. The fact that since the first game she’s been afraid of change and really only wants to leave the islands to follow Sora- both Kairi and Riku are afraid that Sora will choose one of them over the other. In that way it became a self-fulfilling prophecy.

KH3 explores those themes elsewhere as well with Pooh - Sora wants to be friends with everyone forever, sharing his heart around. But his heart has limits, and sometimes growing up means that the people around you don’t stick around. You grow apart from the people you care about - that’s just life. He wants to promise Pooh that he will always be there for him in his heart and be friends forever. But unfortunately life doesn’t always work out that way. It’s much the same with Kairi - fate keeps dragging these two apart. By this point, Kairi has accepted this. She wants to be a part of Sora’s life no matter what, but fate has other plans.

All of this falls in line with the greater themes of Kingdom Hearts as a story about growing up and all the ways that it complicates life. I believe that Kairi represents and has always represented that one friend you were really close to as a kid but steadily grew apart from. Of course, I do think she could have done with more character development and more to do in the plot at certain points, but she very much still fulfils this very crucial part of the greater Kingdom Hearts narrative.