PRC will not allow TW to be resupplied by west simply because legally that means foreign hardware operating on Chinese soil to support separatists during Chinese civil war. Optically that's a none starter. The likely outcome is PRC will mine TW shores and continues to crater TW airfields that TW allies can't supply TW even if they wanted to because no one is going to even attempt to supply under such dangerous conditions, and at TW scale there's need to call on civilian contractors who will nope just like civilian black sea agriculture flows can't operate without RU cooperation. Important point being PRC doesn't have to intercept, it can passively deny via mines and cratering airfields blockade running at scale needed to support the island is not technically feasible. Besides the ludicrous notion of Berlin airlifting an island of 24M people - western global strategic airlift doesn't remotely have capacity even pulling civilian assets. What's most likely going to happen is once TW slowly starves and dehydrated PRC will offer to supply from strait side (being one of the few powers by size and geography that actually can supply 24m mouths), TW genpop by this time may likely be fatigued to point of capitulation (it won't be UKR where shelves still stocked with food and civilians defy with full bellies), and deliver relief along with military, with returning mainland trips exfiltrating foreign nationals using has human shields to limit escalation.

>they cannot win

PRC can very well win against US regional allies, and in many ways, a broader war is preferable because limited war means US IndoPac security infra remains untouched and others in region free to hedge with US security after TW damocles off the table. The greatest PRC strategic vision is to kick US security out of east asia and for that she needs a broad war where PRC demonstrates US cannot fulfill security commitments by destroying a protectorate so utterly that no one else would consider bandwagoning under US security umbrella after TW. Even in case of draw/loss, having opportunity to knock out extensive US IndoPac military infra (i.e. PineGap in AU) cripples US threatre capability for potentially decades. Who wins is relative, one side can win more. PRC and US both losing similar amount of blue water hulls = PRC can STILL assert military projection in her backyard with land based air assets, VS US basically gets kicked out of the Asian power projection and perhaps global hegemony game. The loss is not symmetric.

Also PRC doesn't need USN to protect global shipping, that's more Zeihan wank that hasn't been relevant for decade+. What PRC has been doing is freeloading off US, but it's more than capable to assuming own protection duties.

I've wrote elsewhere about how seriously PRC historically takes nuclear escalation with respect to security interests - it doesn't - having fought with US, USSR, IND, threatened UK, proxy FR over things much less important in TW. US carrier groups are unlikely to threaten mainland with PRC a2ad which again extends to Guam, well past even CSG sprint + stand off extended range. And even lul recent balloon drama aside, PRC rocket force can reciprocate hitting CONUS infra conventionally. If the US takes war to PRC mainland, expect critical infra to be gone on CONUS. It will take a few years for mutual vulnerability to filter way through western analysis, but all the US wank expeditionary warfare is contingent on it being unilateral, with homeland remaining un-disrupted. That's not true with PRC anymore, with PRC ability to strike CONUS only increasing with time, which will greatly circumscribe what the US will do in the TW scenario. And with precise rapid strikes being developed (PRC parlance for prompt global strike), we're talking about every US capital asset being a port visit away from being scrap. Including upcoming B21s that still needs hanger dramaqueen time. West keeps focusing on US deterrence efforts around TW without realizing PRC is also simultaneously building up intervention deterrence. Except PRC deterrence development is much more significant - US could always hit targets in mainland, that calculation was baked it. It's when PRC can hit CONUS that real deterrence math changes.