...Bowser is acting pretty much like himself? That's been one of his most prominent designs. He's actually been monstrous quite a bit, and has only shown a more human side throughout the years. Literally in Super Mario 64, his first 3D debut, he was very very monstrous. Paper Bowser isn't remotely the same thing. His character has evolved, but he actually was very accurate when added. Just cause he doesn't evolve Bowser's personality with the new games doesn't mean he's actually inaccurate. He's not updated to newer stuff, but it's still based upon his canon personality. Now, if you were talking about Lucina...
However, he does massively care for 3rd parties and very often goes for their original designs too. Regardless, Sora was created by Square-Enix, so calling him "a SE character" is not remotely wrong. Nobody is calling him a "SE-owned character", which has a very different meaning in itself. He's also a Disney character. Characters are basically a sum of all their parts when describing what company they relate to. That's not referring to the ownership. Banjo, due to his origins, was a Nintendo and Rareware character too. He's also now a Microsoft character. All of these are accurate statements. And that's what people mean, just companies that are involved with a character directly. SE is still involved, so "was" is a silly point to make. He's still clearly a SE character, including the fact they outright put him on a list of 7 leakbait characters by choice. So they take the fact they're associated with Sora quite seriously enough for catching leakers too. That's a core reason why people still call him one, since they know SE sees them as a part of Sora's overall core history.
They don't need to be involved in licensing. But SE will be involved in the character process. It's extremely rare that the developers for a 3rd party character have zero involvement in a character that Sakurai is working on. There's not even a proper example of where they wouldn't be involved. Either we don't know or we know they're involved. So yeah, Sakurai's going to clearly ask for help from SE with Sora if he is able to license him. He wants the people responsible for the mannerisms, etc.