Sorry, but your submission has been removed because we don't allow hypothetical questions. If possible, please feel free to rephrase the question so that it does not call for such speculation, and resubmit Otherwise, this sort of thing is better suited for /r/HistoryWhatIf.
This is a fun question, and here's my theory-opinion.
There are two main scenarios, depending on who won the Chinese civil war, in this alternate reality.
Under scenario #1, the Communist Party are still the victors, but the KMT were either killed or fled elsewhere. In this scenario, immediately after winning the civil war and after centralizing their national government, Communist Beijing would have absorbed Taiwan into its governing, claiming that Taiwan has always been a part of China, as they claim now. But this sovereignty claim would have likely been challenged by the U.S., who was occupying and creating a new Japan at the time, so that the U.S. could puppeteer its new democratic ally Japan, as part of the American geopolitical positioning in the early stages of the Cold War.
U.S.'s response to Communist China claiming Taiwan would be that China's efforts would amount to an illegal annexation. Further, because the U.S. were the true victors over Japan after WWII, then the U.S. should therefore control / govern Taiwan they would argue, through the American's controlling over Japan. And thus Taiwan would or could have been a proxy of the early part of the Cold War, analogous to and vis-à-vis the Korean War.
Under scenario #2, the Communists lost the civil war and the KMT as victors centralized their national government in the mainland, most likely Beijing but possibly Nanjing. As capitalists, Taiwan would have been a valuable source of raw materials in the KMT's eventual attempts at economic growth, and KMT would thus make the same sovereignty claim over Taiwan. Except, KMT's claim won't be challenged by the U.S. because the geopolitical dynamics and powers in this scenario favored American interests already.
Under either scenario, I would argue that Chinese nationalism and identity would still be strong, and imperial Japanese remnants would still be discarded, but to varying degrees. The KMT would still have gotten rid of the cultural parts of imperial Japanese legacy, but would have kept the infrastructures that the Japanese laid out (roads, schools, railways, communication lines, etc.). But a Communist China ruling Taiwan would have likely destroyed everything Japan, including infrastructure, because a communal society doesn't need infrastructure the same way as a capitalist, free-market society.
Ultimately, regardless of the victors of both WWII and the Chinese Civil War, Taiwan island would always be claimed by someone, because of its strategic location, and a long history of it being ruled by governments abroad. Put another way, Formosa has been, and always will be, claimed as a foreign government's territory.