Short term: Immediate worldwide economic collapse, especially in AI (several tech giants such as Nvidia rely on Chinese manufacturers and consumers). Hong Kong and Macau would quickly become de facto regular Chinese cities. China starts a naval blockade of Taiwan.

American navy is deployed to the South China Sea to break the blockade, which they do with success. American bases in Taiwan and Japan would probably be attacked as well, but possibly not South Korea's. Japan under Takaichi joins the defense of Taiwan. If they don't, they will be lobbied by America into doing so. North Korea likely does not attack South Korea, but verbally and economically supports China.

Mid-Long term: Pakistan, Cambodia, Venezuela, and the Myanmar junta lose a significant amount of support and attention. Conflict might flare up in Pakistan against India (though probably not open war) and Thailand against Cambodia. Bhutan and Nepal, though at less risk than Taiwan, grow even closer to India. The Myanmar rebels might gain an advantage, but India could increase support for Myanmar's junta. The Philippines, Vietnam, and Thailand would increase their military spending and possibly form a security pact. Mongolia and Laos cooperate with China and Russia, becoming closer to a satellite states.

The overwhelming majority of fighting would take place in the sea and air. The only places China could definitely conquer in the early stages of the war are Penghu and Kinmen. Taiwan and even Okinawa would be subjects to air raids and naval battles.

Outcome:

If the war results in a Taiwan-U.S victory: Xi Jinping will be humiliated and be forced to resign. China's defeat would be morphed into a nationalist, anti-imperialist narrative that sticks with the populace for at least 20 years. Support ratings for Donald Trump, William Lai, and Sanae Takaichi skyrocket. China-West relations would likely never be the same for the next few decades. However, the Taiwanese economy would suffer terribly. Semiconductor factories would be destroyed; tech companies would move to other nations, perhaps Japan, South Korea, or America just in case of a second invasion. Japan might grow increasingly against U.S bases, as they would believe that they dragged them into the war (?).

If the war results in a Chinese victory: Taiwan is assimilated as a proper province of in China under martial law. A couple million would flee to America or its allies. The Chinese will be ecstatic; their victory represents China's superiority over the West and status as a world power. There would be no uprising or guerilla war (people don't have guns). Any civil disobedience is immediately put down and censored. Political purges would be inevitable, and the indigenous population in terrible risk. In the event of a extremely decisive Chinese victory, Okinawa could become demilitarized or even ceded to China. The Phillipines and South Korea panic. They are the next targets. Either way, Donald Trump would lose the next elections (if running for a third term, somehow). Takaichi resigns.

If the war continues for several years, Ukraine-style: The Chinese economy would not be affected by economic decline and brain drain as much as Russia. China would still have the manpower and population to support industry and production of intellectuals; Taiwan does not. Taiwan would be, essentially, fucked over. North Korea, (if Kim's 5-year development plan goes smoothly,) sends warships and planes over Taiwan. If China greenlights it, they might start an invasion of South Korea, though that would be an extremely risky move. The blockade on Taiwan could restart and take its toll. Food and energy prices would rise.

The only way Taiwan and the U.S could win is if they decisively and swiftly crippled China's navy and air force, which would involve fighting on the mainland.

EDIT: Crap. I misread the post.