If Taiwan is a Province, then why do they have their own currency, own passports, own army, own government? Why do Chinese laws have absolutely no jurisdiction? Why aren't Chinese military allowed to train there if it is part of China they would be allowed to. Why do Chinese need go through passport control to get to a "province" of their own country? I think you may just possibly have been brainwashed by Chinese propaganda. Taiwan is a country.
Except that isn't what defines a sovereign state. The majority of nations don't recognize Taiwan, they recognize China. Any country that wants to have relations with the PRC must not recognize the ROC. Due to the size difference between the mainland and Taiwan, most countries conclude that trade with the PRC is much more lucrative than trade with the ROC. I don't think it's right that Taiwan doesn't have full sovereignty, but geopolitics doesn't care about feelings.
But it is what defines a sovereign state: "a state with a defined territory that administers its own government and is not subject to or dependent on another power." International recognition is not a pre-requisite, but rather the exercise of sovereignty within its borders. Taiwan exercises sovereignty within its own borders.