Sorry, I have to retract my earlier concession as I had assumed you'd attributed universal powers to Xemnas rather than what you've stated above.
I was under the impression that absorbing KH DID give him universal powers.
and doesn't even acknowledge Sora to have beaten him
That doesn't mean that he didn't get beat, though.
If he'd had any interest in Kingdom Hearts, we have no proof that Xemnas would have been more powerful.
No, Xemnas still would have as said by Nomura. Because the truth is, KH Sephiroth isn't one of the most powerful guys in the KHverse, regardless of how tough his boss fight is.
Even if Kingdom Hearts were a "multiverse" (which it isn't)
Yes, it is. It has multiple planes of existence, which are each assumed to be infinite. They are known as:

Realm of Light
Realm of Darkness
Realm of In-Between
Realm of Nothing

it wouldn't mean the creatures therein are more powerful than any single Final Fantasy universe.
Not something that I ever argued for.

A multiverse would imply several coinciding universes that each play by their own rules.
They do play by their own rules, actually. See, unlike the other realms, in the Realm of Nothing, you slowly fade away until you are completely wiped from existence unless you can remember your past like Ansem the Wise did.
Sora's abilities are not hard to learn
Throwing a dragon into the sky and slicing through seven buildings in the blink of an eye isn't hard?
they come to him swiftly and efficiently and even conveniently as the plot demands.
Which is proof of his amazing growth ability throughout the series.

I mean, in KH1 he starts from being an island kid playing with a toy sword to beating the strongest Heartless in existence in ~23 days.

Then when he lost all of his KH1 abilities in CoM due to Castle Oblivion, he was still able to experience a rapid enough growth to take down Organization XIII's (6th?) strongest member in ~25 days.

Then when he lost all of his Castle Oblivion powers during KH2, he was still able to go from nothing to gaining back his KH1 powers with Limit Form, and then to being strong enough to be able to beat the strongest person in the KHverse. Don't know how long this took, but I'm assuming it's not that much of a difference from the other two.

If you're thinking that I made up these numbers in days, I'm not.

The Reaction Commands in KH2 could tell you that Sora knows how to analyze his enemies' attacks and devise counter attacks. They exist for a lot of normal Heartless and Nobodies, and they exist for every single boss fight in the game. You might think that RCs are gameplay elements, but there are two things that say otherwise:

1. Many of these RCs have cutscenes, and cutscenes are essentially the game's way of showing you what exactly happens in the story. Especially in KH2, the game that has so many cutscenes that the cutscenes alone can pass off as their own game.

2. Many RCs are also unavoidable and are required to beat the story. This is just about every RC in the final battles.

He doesn't gain the majority of his ability through "experience" as Final Fantasy characters would but instead they simply make themselves available when the story decides they're needed.
Yes he does. After every single boss fight in KH2, he gains a new ability. RCs are essentially counter-attack strategies, and they don't just come to Sora because the story makes it convenient. They come to him, or anyone for that matter, as a result of being skilled and having good knowledge of fighting tactics.
Just because his level goes up and his stats increase slightly, doesn't mean he's gaining any new abilities.
I never brought stats into this. But certain things do in fact say that he's gaining new abilities, such as Donald/Goofy handing him Dodge Roll, Cloud handing him Sonic Blade, and the fact that every single boss battle victory in KH2 has him learn a specific new ability. These ability gains are unavoidable elements as you progress through the story, so they pretty much are canon.