K so I decided to take a look through various interviews,
"— I see. Something that’s definitely a hot topic this time is the announcement of the “Toy Story” world. Having been so eagerly awaiting this moment, it’s sort of like a “It’s finally here!” feeling inside.
Nomura: I’ve been wanting to add Toy Story in from since KH2, so even for me, I’m welled up with emotion finally seeing it implemented. For KH3, a Toy Story world was absolutely necessary. With these thoughts, and after many discussions, here we are.
Just like we did back with KH1, we had to relentlessly consult with all related parties… It was quite a long process (laughs). For example, when John Lasseter* had come over to Japan, I was asked about the way I was thinking of implementing the worlds(**), and I would tell him about the types of things I wanted to include, and so on."
So here he directly states just like he did with KH 1 he had to consult with the devs, this would imply virtually every disney world in KH 1 is canon.
"—We were surprised at how the plot of the Pixar worlds were continuations of the original movies.
Nomura: Originally, the basic pattern of the KH series was that Sora and the others get involved in scenes that depict the happenings of the original films. The Tangled and Frozen worlds fit that description. However, with Toy Story and Monsters Inc., upon request from the creators, we went with a pattern of depicting a period set after the movie as an "authorized history." Which pattern a world would follow depended greatly on the ideas of the creators and producers of the movies."
Authorized History is essentially accepted/allowed history, but I want to also note this implies that Monsters Inc is canon to KH along with Toy Story.
"--We heard that the Toy Story world forms also took a lot of back-and-forth with Pixar.
Nomura: Yes. At one point, there was a time when they were going to look like pixel characters. Like pixel art made 3D. As we adjusted them to look more realistic, they began to look more like figurines - which is how they ended up with their current look."
This doesn't prove much, Pixar devs specifically talked with them over Monster inc designs too and they want to make sure the characters correctly fit with the world. It doesn't prove canoncity.
"-With the heart being a major theme in Kingdom Hearts, it definitely fits. The fact that this time, an original story is being prepared is also incredibly exciting.
Nomura: There was huge desire from the Pixar creators to have original stories for both Toy Story and Big Hero 6. So that's what we decided on. Up until now, Sora, Donald and Goofy have always been placed into a well known Disney setting, but this time I'm curious to see what will happen."
Here he directly states Pixar creators wanted original stories for both Toy Story and Big Hero 6.
So basically from what I can gather from these links, Pixar basically allowed Nomura to add authorized original stories within their works instead of the general unoriginal heavily abriged versions of the Disney worlds, and the main claims for canon come from how Pixar discussed with him where they'd want it and how it's not a parallel world, but let's go into the IGN article cause that's supposed to basically confirm it's canonicty.
It's said here:
"...But it’s not as simple as just ‘Disney’ or ‘Pixar’
While there’s obviously a certain amount of movement between projects, both Disney and Pixar keep teams of animators intact after their films have been released – and those teams all have a say on their work being repurposed for the game.
As Nomura points out, those teams can have different takes on the same issue. Take storylines. Some worlds in the game – like Tangled – reimagine the original movie’s plotline, where others – Toy Story, for instance – involve plots set in between the existing movies. Those decisions seem to come down mainly to the creators involved:
“For each different world we had to deal with a different team,” explains Nomura, “and [plotting]" was largely down to what their feelings were on what they wanted to happen. There were some teams that were like, ‘Ooh, if you make a new story, you're going to kind of ruin the world that we created,’ whereas there were teams, like Toy Story, who said to us, ‘Well, we can't have it in that world, but if you want to make a new story, that's fine.’”"
"As explained above, Pixar’s teams in particular could be fairly exacting about what they want their worlds to look and feel like – but some decisions were subject to major discussions well before they became reality.
Nomura explains that his vision for Kingdom Hearts has always been that Sora and friends canonically arrive in Disney’s worlds. That didn’t suit the Toy Story team. “When I first brought this to Pixar and I asked about doing that, they were like, ‘Actually, no. The Toy Story story is complete. It's a complete package the way it is, and we can't really change that.’ I told them if I'm going to do this in the Kingdom Hearts way, then it's going to become a case of, ‘Actually, Sora and his friends did come into the world.’”
The solution became to place the plotline between Toy Story movies (specifically 2 and 3), satisfying Nomura’s vision, Pixar’s restrictions and creating a strange extra consequence: “I said, ‘Okay, so is it fair to assume that Woody and Buzz, and friends, remember Sora and everybody coming? Is it part of the story now?’ and they were like, ‘yeah,’ and I was kind of like, ‘Oh! Okay.’”
So this is taken completely out of context, note the original statement, that Nomura's vision for KH is that Sora and co. canonically arrive into a Disney world and Pixar saying no to that, and they only accept it being apart of the story once it's fit in-between the two movies. Essentially what's "canon" here is from Nomura's vision, they're not outright saying KH is canon to Toy Story, they're saying for what Nomura's vision is for the Toy Story world it's canon. Or else Bob is arguing for literally every Disney world to be canon.
So like I've said, this is a one-sided canon, not a double-sided canon.