1 and 2 are the biggest reasons by far and matter a lot. Dictators are people too, they are susceptible as anyone to their minds being poisoned by too much nationalism. And even if it wasn't for that they would still view it as a way to get back flagging support from a nationalistic public(even dictators need a minimal amount of support from the population).

They do see Taiwan as an internal matter, that's the problem they don't recognize this sovereignty and don't like or understand Democracy. It's like Russia with Ukraine but they'll also claim Taiwan isn't a country because even most western nations technically don't recognize them. It makes me think we made a mistake not recognizing Taiwan as it's own country back in the 90s when China was less powerful.

Just answering your question "What I still don't get is what could China possibly want with Taiwan?".

If you don't believe the rational I sketched, informed by analyses such as that by the Council of Foreign Relations[1], you can also learn more by reading directly from China's Mission in the EU about the China One principle: http://eu.china-mission.gov.cn/eng/more/20220812Taiwan/20220...

[1] https://www.cfr.org/backgrounder/china-taiwan-relations-tens...

Nationalism makes it very easy to make it seem like (1) and (2) matter even if they don't.

If you want a semi-serious example, check the "Taiwan #1" gaming video on YouTube for a taste of Chinese nationalism.

Read certain declarations by Chinese ambassadors in Europe for more serious nationalistic takes.

Throughout Chinese history, all invasions of China from the sea had a staging area in Taiwan.

This is the main reason.