Permanently stationing our best and brightest looks anything but ambiguous though.

Yes, the US' ambiguity has been slipping a little bit of late, but it still compatible with their long-term held position. The US has consistently (over decades) both not recognized PRC sovereignty over Taiwan, while also not recognizing Taiwanese independence.

However, US actions have also been clear. In 1996, the US sailed a carrier battle group right down the straits when things get testy. The US has been selling weapons to Taiwan for decades. The US has enacted export limitations against one country, but not another.

Functionally, this action did not declare war on China. Yes, China leadership could find a way to stretch this into "war", but they also could have stretched any of the other things the US has recently done (including Biden straight up saying that the US would intervene if China invaded).

Yeah diplomacy isn't a series of automatic actions based on flow-control or checklists. Just because you crossed some lines doesn't mean the other party will respond exactly how they will.

That being said, credibility is important when making threats. And letting your lines in the proverbial sand get crossed, moved, erased, redrawn, etc. endlessly can make for some ... interesting geopolitical situations.

The Taiwan Strait is 81 miles wide at its narrowest point. Imagine the reaction in America if China sailed a carrier fleet 81 miles off of New York.

It's a very small force, no threat to China's military.

unfortunately its sacrifices to give cause to war

The troops stationed there are not meant to hold off a mainland invasion by themselves.

The presence of US troops means that if China attacks, the USA is going to suffer military casualties, so there is almost certainly going to be war between the CCP and the US.

Without US troop presence, things are more ambiguous.

It's called "Tripwire force".

https://en.wikipedia.org/wiki/Tripwire_force

These are trainers (if that article is correct - I have no idea of their credibility), not a tripwire force.

The two are not mutually exclusive. If China invades and kills US soldiers in the process, training team or no, that’s still gonna be casus belli for the US.

I don't think so. Iranian proxies and others have killed US soldiers recently without starting a war.

The US had a training team in Georgia when Russia invaded.

The trainers turned themselves over to the Russians, and were interred (at the Ritz) as neutral soldiers.

A training team can be a tripwire, or not.

Again, ambiguity.