Taiwan is in 'China' in the same way as both North Korea and South Korea are in Korea.
The difference is that the People's Republic of China (what 'China' usually refers to) has decided that the Republic of China has ceased to exist in 1949 (Taiwan is the last remaining territory controlled by the Republic of China) and that they are strong enough to largely 'enforce' this policy on the world stage.
So, of course for Chinese this is a domestic issue.
The West cares because the PRC is an adversary and Taiwan has a strategic location on maritime routes to East Asia.
Yes, but my point is that most of the world, including the US, has agreed to acknowledge the One China policy as correct in order to access China on a diplomatic and trade basis. Hence why it's not so easy to resolve.
The difference being that the world never agreed to the idea that France was a part of Germany. The world has for the most part agreed that Taiwan is a part of China. It is what it is. Whatever people's personal feelings might be, that is what most of the world has agreed to at an international diplomatic level. Only insignificant countries like Paraguay have decided to consider Taiwan an independent nation state.
Taiwan is factually an independent state and in practice recognised as such by everyone, including the PRC. "Nation state" has a different meaning and that's not really the case for Taiwan.
There's a lot of propaganda like for HK, which is popular with the Western public who is naive and not well informed (as all public)
We can go back and forth about this, but political feelings aside, although Taiwan acts like an independent state and has its own government, no important independent state treats it like an independent state, including the US. Donald Trump is the first president in four decades to even send a cabinet-level official to Taiwan when Alex Azar went to visit last month. It is what it is. Whether you like it or not, no important country has official diplomatic relations with Taiwan because they've all agreed to the One China policy. It is partially because of this One China policy that Taiwan's economy has deteriorated so much, they are not on equal footing with other countries in being able to develop trade agreements with other nations. China has them boxed in.
The difference is that the People's Republic of China (what 'China' usually refers to) has decided that the Republic of China has ceased to exist in 1949 (Taiwan is the last remaining territory controlled by the Republic of China) and that they are strong enough to largely 'enforce' this policy on the world stage.
So, of course for Chinese this is a domestic issue.
The West cares because the PRC is an adversary and Taiwan has a strategic location on maritime routes to East Asia.