It has been confirmed that the Shibuya which Sora will be in Kingdom Hearts 4 is not related to the Shibuya in The World Ends With You. This would have been an easy things for fans to expect, but more information about the somewhat complicated issue of just what Quadratum is in Kingdom Hearts has come to light from series director Tetsuya Nomura.
This differing identity of Shibuya and Quadratum may come as a surprise to Kingdom Hearts 4 fans, as two previous installments of the game, Kingdom Hearts: Dream Drop Distance and Kingdom Hearts 3, both had references to (as well as characters from) the series guest star in the main story. Speculation had risen on whether the sequel would be taking place in the world of The World Ends With You due to characters Neku, Shiki, Joshua, Beat and Rhyme appearing during the events of Dream Drop Distance.
But Nomura confirmed in an interview with Famitsu (as reported by Polygon) that these locations are two separate entities, so it seems that a crossover with The World Ends With You isn't in the cards for Kingdom Hearts 4. Nomura reported during the interview that main character Sora is located in what seems to be an alternate reality of Shibuya called Quadratum in the trailer for Kingdom Hearts 4, and this will be a subject of narrative contrast in the game itself.
Kingdom Hearts 4's Quadratum Is The Real World, Not TWEWY's
While stating this, Normua specifically confirmed that this Shibuya is not the same location where the Reaper's Game takes place. This would make the location in question unique in that it is not only unrelated to the game franchise that was expected, but that it also is considered its own universe and may not even be related to any franchises owned by Square Enix or Disney.
The Shibuya Sora awakens in will be his base of operations for the early game. He will spend time in the apartment shown in the trailer, and the world of Kingdom Hearts 4's Quadratum seems to be designed to be based in the real world. Highways, office buildings, and a modern style were shown in the trailer with a new, more realistic style versus the previous fantasy and cartoon-esque art of previously visited worlds. This seems to place him in a real world more akin to the real world versus well-known movie universes or game franchises, and could hint towards a different selection of worlds Sora could visit in Kingdom Hearts 4 outside of Final Fantasy or Disney franchise locations.
Given this, it still doesn't seem impossible to see characters from The World Ends With You popping up. The last place the characters were seen was the parallel worlds, during the trials Riku and Sora were tasked with during Dream Drop Distance's plotline. Neku stated that they were there due to a trial (similar to a Reaper Game) that he only had forty-three minutes to complete when first meeting Sora. After betraying Sora and being forgiven, Neku and his partner Shiki invited Sora to come and visit them in Shibuya later on when he was done with his journey. This could still be brought into the sequel, as the Kingdom Hearts series makes a habit of offering different worlds to explore. The recent confirmation of Strelitzia, a character from Kingdom Hearts Union X, also indicates that Kingdom Hearts 4 won't be afraid to bring in more characters unique to the universe - and outside of the Disney franchise entirely.
Source: Famitsu (via Polygon)