China has been studying the invasion of Taiwan since the late 1940s, and all the geography and problems that go with it. In the last 20 years, they have devoted their entire military industry to solving those problems, churning out all sorts of new capabilities they never had previously, and all of them are purposed for overcoming the problems of this invasion. And, they have rehearsed and gamed. Gaming allows "safe failures," and if done correctly, identifies mistakes, weaknesses and priviously unconsidered additional obstacles which need to be addressed. They are increasingly more
and more prepared to tackle a task you assume is impossible, or too dificult. Our own wargames have shown China can invade and win. China can also blockade without invasion. They can launch an intense missile bombardment to destroy Taiwan's infrastructure. They can just use diplomacy and wait it out. It does have options. Which one it will choose is only known to a few top officials in China itself. Your assumption that it is too difficult and costly reassures you that all's well, and diplomacy will prevail (and I am a bit paranoid.) Yet, their statements and actions consistently show that they are focused on a military solution which is plausible, and actually winnable. D-Day was about 82 years ago. Times and weapons have changed.

It boils down to whether or not China chooses to use a military solution (which encompasses not just an invasion) and the factors in that decision are multiple. IF they choose to do so, then wargames have shown that Taiwan will eventually lose if it receives no allied military assistance. China calculating no one will have the will to come to Taiwan's aid could trigger any of these military solutions from them. IF they then miscalculated (no one has ever done that in the history of warfare, of course, so I am just plain nuts here) and the US does show up, then two large nuclear armed powers are now in an open war with each other.

One wargame which was run specifically tested the possibility of a US-China conflict over Taiwan going nuclear. Understand that you are right...Xi's regime is over if this fails, so then "failure is not an option." Once China commits, it will not quit. It must win. That increasing desperation as things fall apart should they have miscalculated is what the wargame found pushed China's military leaders into the nuclear option/decision. In 15 runs, a nuclear holocaust happened 3 times.

https://www.csis.org/analysis/confronting-armageddon

One fifth of the time neither side was able to contain, deescalate, or deter enough to prevent a nuclear war.

IF China miscalculates, uses military force, and the US responds after all, simulations do not show anything good resulting, with nuclear war also possible.

I am relaxed. IF a military conflict ensues. No guarantee at all that will happen. In fact, the first wargame scenario I read had China conclude war was too costly, and resort to diplomatic pressure. Darker games soon followed. (The ones run by our Pentagon were the grimmest of all.) All hypotheticals. Nothing about war is predictable. A lot of IFs between us and a nuclear conflict. I am not living my life in a paranoid terror of being nuked. I honestly could care less. During the Cold War, we practiced getting under our desks in school. We saw saw civil defense films on what to do when we saw that big, blinding flash when the bomb went off. I have spent a lifetime in the shadow of "imminent nuclear war." Yawn. Que sera sera. Some find comfort convincing themselves we are too bright, and could never do this to ourselves. I can't possibly hold that view. Nothing I see in the species supports that conclusion. But, it is moot to me whether we do it or don't. What good comes from worrying over it? Life goes on until it doesn't. Life is my focus, while I have it.