What kind of line is "once china solves the taiwan problem"? You assume that they will take Taiwan. Have you not been privy to the utter embarrassment of a continental power trying to take Ukraine right now? China is very aware of the isolated situation Russia is now in. They have desire to be in that situation.
Noone is letting China "solve the taiwan problem" like you said.
Such inflammatory language.
The Ukraine invasion is the biggest boost to China's Taiwan invasion plan ever.
If the world reacts to a Chinese invasion of Taiwan the way we have reacted to Russia invading Ukraine, China will consider that a great victory, and might be able to take Taiwan.
If the US, Japan, and Korea do not commit fully to naval interdiction and blockading China from attacking Taiwan, Taiwan is likely to fall eventually.
China is not Russia. Xi somehow is not as utterly isolated from reality as Putin is. Putin didn't even know that Ukraine would resist, and was entirely convinced that Ukrainians would welcome them. China can build new equipment, and new modern equipment at that. Russia can barely manage to bring ancient tank hulls up to 2000s level and send them to the front line. They are also running out of old hulls to do that with.
China has a sizeable and meaningful air force, modern battlespace management that was shown effective by Pakistan's use in their recent conflict.
Is the current US admin actually competent enough to protect Taiwan even if they want to?