The Treaty of San Francisco did not mention upon what country the sovereignty of Taiwan would rest. Many people thus claim, as per international law, the legal status of Taiwan is undetermined. However, some people argue that the Japanese Instrument of Surrender explicitly agreed to fulfill the terms of the Potsam Declaration, which in turn incorporated the Cairo Declaration, which stipulated Taiwan's return to the State of China. The problem is, the said declarations were not binding by themselves. What country holds the sovereignty of Taiwan now? Is Taiwan's legal status still undetermined?
Short answer is "China"
It's therefore an internal matter for China to sort out. It just happens that there are two governments that have opposing claims to be the "Government of China", and neither one looks likely to cede the Chinese territory that it holds to the other any time soon.
A matter in international law is "determined" if all relevant parties agree on the determination. As both the ROC and PRC are relevant to Taiwan, and they don't agree, the status is undetermined. The US and other powers have made it clear over the past 70 years that they have no interest in getting involved, but are quite happy to work with both governments.
It's pretty clear that the Japanese only agreed to return Taiwan to "China" and not to the PRC or the ROC government. Nothing in the various treaties binds any country's right to recognise or not any government on the Chinese mainland or on Taiwan.
No Chinese government was a signatory to the Treaty of San Fransico, so cannot be bound by any of its terms.
I believe this question shows some misunderstanding about what international law is and what it is not.
By and large, international law is the customary law about how sovereign nations deal with each other. Historically it did not care much how nations deal with individuals or how nations arrange their internal affairs. This concept is known as Westphalian Sovereignty, after the treaties which ended the Thirty Years' War.
International agreements which restricts how nations can deal with their citizens are more recent, like the Helsinki agreement, the Responsibility to Protect, or the International Criminal Court. Their ability to override national sovereignty is far from certain.
So the question becomes: Is there one China or two?
De facto, there are clearly two sovereign Chinas. But at this time both of them consider that there is only one China, that the Chinese Civil War is not really resolved, and that the other government which controls part of China is not quite legitimate. As long as both Chinas agree that legally, there is only one China, there is only one China. Nobody else has the "standing" to complain.