Olympus- When Sora asked Hercules how he regained his strength in order to save Meg, Hercules says that when he saw that Meg was in danger, he wanted to save her with all his heart. Sora cites this saying several more times in the game, with a couple of these instances directly linking back to Hercules. The idea of accomplishing anything with all of your heart for Sora led to him reuniting with & saving Kairi, similar to how Hercules was able to save Meg's life by risking his own.
Toy Box- The carving of Andy's name being on the foot of Woody, a toy who misses the aforementioned individual that they care about, is similar to the carving of Sora in the Secret Cave that Kairi went to after she was separated from Sora after all of the worlds were restored. Hopefully it's not too big of a stretch to say that Kairi really missed Sora during this time. In Galaxy Toys, the blue haired, yellowed eye Angelic Amber doll was defeated after being under the influence of darkness. This leads Buzz to say "What if all we end up just like her? Forgetting ourselves & attacking each other? What if I get taken over & attack you?" Later on a blue haired Guardian of Light subcums to the darkness, is given yellow eyes, forgets who she really is emotionally & attacks her own allies.
Arendelle- Anna, in a last-ditch effort, puts her entire body at risk to protect someone she cares about by preparing to take the blow of a blade from someone who once presented themselves as an ally. For Sora & Kairi vs Terranort, this moment is less of a callback & more of a scene that is similar or analogous to another, also known as a parallel.
The Caribbean- As Gibbs said at the end of this world "Just wed, and now she & Cap'n Turner must live in different worlds". The two lovers, bound together by a promise, are now separated from each other & can only be together for one day every 10 years. Sora & Kairi's destinies are also intertwined & bounded together through the sharing of the Paopu Fruit. But after Sora changes the destiny of himself & his friends, he too is separated from his world & spends his last day with the person he cares about the most while also being able to tell her one last thing, despite his previous belief that one day isn't enough time for "hearts to say what's true".
Kingdom of Corona- The full lyrics for Rapunzel's Healing Incantation is "Flower, gleam and glow, Let your power shine, Make the clock reverse, Bring back what once was mine. Heal what has been hurt, Change the Fates' design, Save what has been lost, Bring back what once was mine. What once was mine." The shining heart fragments of Kairi, which merge together to form a flower, reverses Kairi's death at the hands of Xehanort, much like Eugene's death at the hands of Mother Gothel. This was accomplished by Sora using his power to go back in time, challenge his fate, save/heal the ones who have been hurt, & bring back the person he wants to be in his life.
Monstrpolis- Randall's poignant speech about causing one so much emotional pain that it breaks their hearts & affects them deeply, is very true for Aqua, who is suffering from PTSD & for Sora, who witnessed the people he believed were the source of his power, get taken away. Out of all these examples, this is the one that caused me to put "Some of these might be a stretch" in the title in the first place as Monstropolis wasn't the only instance of characters telling Sora that something sad was going to happen to him. So the concept isn't entirely unique or specifically derived from what Randall said. Nevertheless, Monstopolis is a Disney World & thus qualifies for this collage. And given that this world had a direct influence of the revival of an original Kingdom Hearts character, it really wasn't necessary for this world to have a parallel since it had a direct, obvious & clear influence on the plot as a whole.
100 Acre Woods- Sora's picture disappeared from the cover of Pooh's book. It isn't that big of a stretch to believe that the reason why Nomura did this was to foreshadow Sora's fate at the end of the game. To add on to that, Sora assures Pooh that he'll never be apart from Pooh as long as the bear remembers that Sora will always be in his heart. If what Sora said is true, it isn't unreasonable for Kairi to believe that there may be a clue in regard to finding the whereabouts of a loved one who has disappeared within her heart as well.
San Fransokyo- To experiment with the nature of controlling one's heart, the Organization obtains a vessel (Baymax 1.0) and a "heart" that is filled with dark emotions, which happens to belong to someone who was once the ally of the heroes who know that the former ally's heart is more than just darkness. Through the replacement of darkness with light in the vessel's heart, the past ally is restored to their original, defender of light selves. Terra & Xion go through the exact scenario that Baymax went through.