You're arguing semantics. The west refuses to recognize Taiwan as the legitimate government of China and refuses to recognize it as an independent country.

Whatever they claim, the west (and most of the world) due to Chinese leverage/power refuses to recognize.

Taiwan meets all the criteria for being a state. It controls land, population, it has a military, it has a government, currency, passports etc. etc. It's a de-facto country/state.

It's not semantics if Taiwan itself does not claim independence.