I think beauty is more 'excellence.'

This seems to mostly work, but I suspect that's probably because 'excellence' pretty much means "a lot of some quality" and it turns out that an unexpected excess of some qualities is beautiful. But I wouldn't think all excellence is beautiful? Like, I can think of Olympic sports where the winning performance wasn't beautiful even though it was excellent. Or even some event like getting a 100 on test, it might be excellent, but I'm not sure most people would call it beautiful.

It seems like excellence and beauty are probably overlapping or correlated, but I wouldn't define one by the other.

I don't see how a beautiful painting makes something 'complicated' easier to process

I think the idea is that the painting itself is easier to understand than expected. For example, this is one of my favorite paintings#/media/File:Wheatstacks(End_of_Summer),_1890-91(190Kb);_Oil_on_canvas,_60_x_100_cm(23_5-8_x_39_3-8_in),_The_Art_Institute_of_Chicago.jpg), and I always had a hard time describing what I like so much about it. Especially since if you focus on any one part of it, it's a mess. When I examine the details they seem almost childish to me, just a mish-mash of smudges. And obviously they're not, they all work together, but I could've never predicted that.

Maybe more importantly, despite the fact that I've never seen that kind of field before, it makes me think of this simple rural life and what it feels like on a late summer afternoon. It's not a picture perfect representation, but it still evokes feelings that make it very easy to understand why someone would want to paint this scene.

And it doesn't have to be messy of imprecise either. Very detailed paintings can obviously be beautiful too. And while the way it's done is very different, the feeling I get, of unexpected recognition or understanding is actually very similar. And it's a feeling I'll get when someone explains something in math or physics or chemistry very well too. That seems beautiful to me too, when an idea 'clicks' together just right, and it becomes clearer than I thought would be possible.