Don't worry they'll just call it a "quarantine" or something. That's been the international standard since 1962.
Why ships?
It would begin with several hundred aircraft taking off and airlanding troops about 20 minutes later, with the ROCAF and ROCN destroyed on the ground and at port ideally, as the ships are for the follow-on forces. The pier boats are the equivalent of the JLOTS piers for offloading Chinese versions of the LMSRs. Taiwan just sucks and has really shitty coasts so you need a really big pier to land anywhere outside of like three tourist beaches.
The PLA has a really clever plan where they're just going to do massively big huge exercises every few months, or every year or so, and one day one of them will just be the actual attack. Everyone will realize this is actually it when they don't turn around at the 40-50 nautical mile mark. Maybe the U.S. will realize sooner and send a desperate message to Taiwan who will ignore it or blow it off. This masterstroke of strategic genius worked great in 1973. Still worked in 2022. I don't think 2027 or 2032 or whatever will be much different.
The PRC isn't interested in being a global maritime superpower at this juncture. It's interested in securing its backyard, winning the civil war (i.e. subsuming Taiwan/ROC by any means necessary), and pressuring Korea, Japan, and the ASEAN + AUS/NZ into a free trade bloc/pact. Effectively, it wants to remake the Co-Prosperity Sphere, but by way of trade rather than war.
The U.S. also isn't going to seriously diminish its global force numbers for the sake of Taiwan. It has the Second Island Chain if it really needs to knuckle down. Third, even, if it just wants to defend its own sovereignty. PLAN at most has to munch through 3-4 CVBGs, a few convoys and escorts, and like a couple dozen nuke boats; and basically the entire immediately deployable U.S. Air Force.
If they eat that and still want more then it'd be time for horizontal escalation along neighboring theaters like India-China Border, Central Asia, ASEAN border, Korea, etc. No use throwing more ships than are already in 7th and 3rd Fleet, when it's clearly not working at that point, and it's time to start leveraging stuff like Quad and putting CIA direct action teams on the ground in Uzbekistan to blow up Chinese trains motoring towards Ukraine.
Welcome to WW3 at that point.