Does your country recognise Taiwan an independent country? Does US recognise Taiwan an independent country?
no, but we've been playing a delicate dance of strategic ambiguity for quite some time now.
we're fine with recognizing one China policy , what we don't like and don't want to happen
is China having an actual control of the Island, because that will make China a more dominant power in Asia that it's already now. Taiwan is key to keep China from venturing too far out to the seas.
hence a strong Japan supported by an increase of defense budget will be an outmost importance into keeping China's hand on Taiwan, because that will increase China's calculations on military operation to take the island.