In the "do other countries recognize Taiwan as a country" sense. Generally speaking, the answer is that they don't.

That means Taiwan's independence is only de facto, not de jure, and that is a very bad thing for Taiwan's prospects. Particularly in a world where China now has much more economic power than Taiwan.

I'm not talking about "right". Like I said, I think Taiwan should be independent. But, I'm not optimistic about that continuing to be the case over the long run. China seems to really, really want it, and to be patient about it.

https://en.m.wikipedia.org/wiki/One-China_policy

With all due respect, the difference between de facto and de jure is just smoke and mirrors. Taiwan has been an effectively independent nation for over 50 years with fairly well defined borders and an inept organization like the United Nations is hardly your golden ticket for staking your sovereignty out on the map when the world is ruled by money, guns, drugs, and superior technology in approximately that order.

The United States still has enough force in the area to force the PRC's hand if it invaded Taiwan tomorrow, but quite frankly I think Taiwan has better prospects of seeing the next 50 years as an independent nation than the United Nations does existing in 50 years.

Prior to the Japanese takeover of Taiwan in the 1930s people considered Taiwan part of China. After Chiang fled to Taiwan and placed himself in power he called a Taiwan the Republic of China. The PRC constitution makes it clear that they consider Taiwan a province of mainland China. After many decades of domination by Japan and Western powers it’s understandable that many leaders in the PRC want a status quo ante with regard to Taiwan. Wether one agrees with their stance or not it is certainly understandable why they think the way they do. Also, for a while it was U.S. policy that there be one China. The issue is murky enough that the U.S. still does not recognize the ROC.

And Taiwan claims the mainland, Mongolia, larger portions of Manchuria than even the PRC claims and has overlapping claims with the PRC in the South China Sea. The Republic of China Constitution makes it clear they consider the Mainland Provinces to be part of the Republic of China. After many decades of domination by Japan and Western powers it's understandable that many leaders in the ROC want a status quo ante with regard to mainland China. Whether one agrees with their stance or not it is certainly understandable why they think the way they do. The US doesn't officially recognize the ROC but it does maintain a military presence and agreement with the ROC government.

The difference is there is a large fraction of the population in Taiwan that is willing to trade away all of those claims including their claim to the name of China and become an independent State outside of China.

I mean, China may want that, and they may eventually achieve it, but I think it will require something not far short of complete eradication of the Taiwanese to do that, which to me is probably the determining factor in what I consider "independent". As to de jure, quod jure? I don't think the historical record is in dispute over the ownership of Formosa/Taiwan. It's not that might makes right, it's that might can table the discussion, or rather slab it, and I'm sure that if China does bring those sorts of arguments to the table, their rights will be recognized by other nations, the same as was done for Tibet. But until that actually happens I think that it's only consistent to consider Taiwan an independent state.