There are several things at play here, and going in different directions:
1.the PRC's window for invading Taiwan is closing due to internal demographic issues
2.the people under the power of the PRC are eager for it (because they don't understand the costs)
3.Taiwan is vulnerable in some ways (their own demographic issues, their own lack of experience problem,their own "paper tiger" problems)
BUT
4.Taiwan is not vulnerable at all in some ways (very important ways, 110 miles of ocean is a LONG way to invade across)
5.the US/West(+Japan,S.Korea and our other east Asian allies) won't be keen on it (WWIII only starts if the PRC thinks us sinking some troop carriers is worth committing suicide over)
6.maybe they'd try it if they could be sneaky about it, but that is 100% impossible and we'll know about it for months before they'd be able to initiate it. There is no way Taiwan won't be able to defend itself with 67 days notice.
no, they won't invade Taiwan any time soon and if they do, it will be very VERY bad for them.
I think that's a pretty good overview, but there are a few other factors, or expansion on points you made:
A change of leadership in the US to a more isolationist government could convince them we won't intervene, even to the extent of the limited support we've provided to Ukraine, which could influence their decision.
Xi is a dictator who's been in power for a little over a decade. That's the point where "dictator disease" (making crazy decisions because they've become disconnected from reality) starts to set in. And if his popularity and government starts to stumble, the 'short victorious war' idea can become tempting.
Taiwan has made itself a key part of the global economy (TSMC makes
half the world's semiconductors). Maybe that won't be true in 10 years, but it is right now. That gives the world immense incentive to support Taiwan, makes the cost of an invasion a global thing, and gives China an incentive for a peaceful reunification (invasion would kill the goose laying the golden eggs).
As others have pointed out, Ukraine is a sharp reminder of how badly a short victorious war can go.
Jump-starting an invasion cold isn't easy, and it will go much worse than an even moderately prepared one, but they could try it. One way for the PRC to have their cake and eat it to is to run invasion-prep drills (which they already do) and turn one into the real thing. It won't be as effective as a well-organized invasion, but it will be better than a cold start. (Still a disaster even if they "win", I'd guess, but they may disagree.)