What do you think U.S. could do to influence Taiwanese public opinion ? They already played the HK card. Perhaps a Biden visit before the election and daring China to react ?
Public opinion doesn't matter. America can force the issue because this isn't a public opinion contest, its the leadership choices of an US sponsored warlord. But if America makes a poor choice, it could cause unrest, which will of course harm the chances of an useful auxiliary force when they start a SMO later.
China will have to handle the overall situation with care, because US staked so much of its national prospects on building this case of annexation. However, precisely because they staked so much, this will greatly backfire in the form of a domino effect on America if they fail. They've effectively tied their national fate to a foreign warlord that is a mere 150km from the Chinese Mainland.
So while it is the more just option to just kill whichever American intrudes into the country, it's not the way China can maximize the potentials in the situation. Instead, China must build its own case that both dismantles the massive investments America has made in their own case, and will at the same time capitalize on the payoff once all bets are off to push America as far back as possible in one sweep.
Ideally China can use the momentum from a defensive war to perhaps counter annex American territory and/or force the dissolution of American client states. By casting America as an instigator of war in "peaceful Asia", it will be possible to force former US dependencies to reject US publicly. Alternatively, it will cause the more fanatic among them, for example Japan and the Philippines to double down, which means conversely China can rally their historic enemies in ASEAN and Korea into a tight bloc.
Mainland China depends nothing on Taiwan in terms of materials, industry or even gdp, which means it can essentially be employed in a Stalingrad strategy, where all the fascist armies of Asia will be drawn into a meat grinder with the promise of "a breakthrough" against China if they win, even as the status of Taiwan does not really impact the status of the mainland. By the time their invasion fleets have all been sunk, there home territories will lay wide open. Just like how German territorial greed led to all of East Europe coming under Soviet rule, the greed of America could open a similar path to China, which would otherwise be unthinkable.
All of that would depend on how well China can build it's "case" of both enticing America but at the same time ensuring they are deterred enough to not do anything before the right preparations are finished.
