There has been a native population with their own governance for most of its history.
The Austronesians of the main island lived on a couple of other islands around the mainland, but their inhabitance did not match 1-to-1 with the borders of the province of Taiwan. I agree with you that there was a country (and a nation) that the indigenous Austronesians of the region comprise, but that county is not Taiwan and that nation is not Taiwanese.
There have been some smaller trading outposts from the mainland Chinese over the course of history, but the Portuguese and Dutch traders actually had more influence on the island than those Chinese traders who carefully avoided conflict with the native population.
Correct, the Han Chinese were not anywhere near as brutal colonizers as the Europeans were. The Dutch in particular hunted the Formosa sika deer nearly to extinction. What that shows, more than anything, is that the Europeans shouldn't be trusted in any of their positions relative to the region since they've been violent psychotic extractivists for 6 centuries and their only motivations are their own personal enrichment and the total subjugation of everyone else.
The claim over the island by the Chinese empire ever only existed on paper until a brief period in the late 19th/early 20th century when they tried to brutally colonize the island
Half truths are the worst kind. The Chinese empire invaded the region specifically to kick out the Europeans. Like, it's very explicit that the purpose of the invasion was to get rid of the Dutch East India Company. Europeans went out colonizing proactively and committing genocide because their pope said they should. The Ming invaded Formosa to get rid of foreign invaders. That wasn't in the late 19th century. The Dutch surrendered in 1662. Ming China held Taiwan at that moment. Qing China held Taiwan 20 years later when the Ming loyalists officially surrendered. When that occurred, there was a debate as to whether or not they should maintain occupation of the island. Some argued it wasn't worth it. But the argument that won day? If we don't hold, the Europeans will come back, establish their military bases on it, and attack us. Does that sound familiar? Because it's literally the exact same argument that's being made 400 years later because the Eurocentric empire is STILL establishing military bases in the region with the intent of attacking the mainland.
The Han Chinese occupation of the island is a relationship of settler colonialism. The Austronesians are the indigenous. The Han Chinese that live in the province today are not entitled to a distinct national self-determination. They are part of the Chinese nation. Taiwan seceding from China would be even less legitimate than the European colonists seceding from England because the colonists were not operating as a 70-year protectorate of a world power on the other side of the world with ZERO legitimate claims or history in the region.
I would LOVE to see to Taiwan decolonized, the place names of the Austronesians reestablished, the nation of Austronesians self-determined and self-governing. But we're not going to get that by having a bunch of comprador Han Chinese in the province align themselves with the most genocidal military in the world that continues to exterminate the culture of its own indigenous people. It's only going to happen through successive resolutions of contradiction, starting with the end of the Eurocentric empire's presence in the entire region, including The Phillipines, Indonesia, Korea, the province of Taiwan, and the Western Pacific ocean. When that happens, and China has organized Taiwan province under it's centuries-long demonstrated and proven One Country Two Systems approach, then the conditions for addressing the colonial contradiction will emerge and the work can begin. But America ripping the Han Chinese into two countries, one of them a protectorate and a proxy and the other a mortal enemy, is just a continuation of 600 years of brutal European empire building and it needs to stop.