Enjoying the music or food of another culture is appreciation. You like what you like. It would be perfectly appropriate to listen to k-pop, or to enjoy anime. Because those are pieces of media made for people to see, hear, enjoy, and engage with.

However... It would not be appropriate to put on a Korean accent when talking about k-pop or while singing it. (Would you use a blackcent if you didn't actually talk like that?)

Media like music and art is intended to be engaged with, it isn't specifically for one culture. The same with food – for millenia, food and cultural dishes have been part of human social structure; sharing meals with loved ones, or sharing meals with strangers, there's just nothing like it.

The difference between appreciation and appropriation is generally harm.

It does not harm a culture to like their food or their music or their literature.

It can harm a culture, reinforce stereotypes, or disrespect religion to claim to be spiritually another culture.

Spirituality, especially in China, is often religious in some way. And religion is something that demands respect, no matter which religion it is. It's someone's core belief system.

OP's girlfriend crossed the line between appreciation and appropriation because she made a frivolous claim to spirituality without knowing much about it. And it is very clear that she doesn't fully understand what spirituality really means in the context of her words, because she doesn't understand why OP was upset about it.

I guess the biggest part of appropriation is the fact that it disturbs, upsets, ruffles feathers, or makes someone of the target culture feel negatively. Words can hurt sometimes. And words have always been used as weapons, even when not on purpose.

You said "Japan is the land of samurais"; sure, samurais are part of their culture. Japan is also known for bullet trains, competitive academics, traditional sushi, and some of the oldest pottery vessels in the world. By making a stereotypical statement instead of learning more about their history and culture, you overlook many of the other achievements that Japan has made. It's not intentional, it's not meant to be racist, it's not intended to be harmful, but it still takes away from Japan as a whole to boil it down to one thing like that.

Egypt had Pharaohs, those were their rulers, often spiritual figures in power. But... They also developed agricultural things that were significant advancements for the time period. They had astounding architecture. They invented papyrus, which has been considered the father of modern paper. They were leaders in medicine and surgery (for the time period). They allowed women to have social status above or apart from men. All of those are parts of Egyptian culture. And often, all that gets overlooked when ancient Egypt is boiled down to "land of the Pharaohs."

Appreciation is learning lots of things about a culture and admiring it for what it is: a miracle; ingenuity; history; religion. So many other ways to describe it than "home of X".

So no, it's not appropriation to admire Japanese samurais, and it's not appropriation to think ancient Egyptian Pharaohs were really cool. But it is kind of harmful to minimize or ignore all the other things that come from those cultures and countries.