So what are the JS Kaga and Izumo then?
Just to understand then, any western or western allied country which builds aircraft carriers: normal and needed to project power.
Any Chinese aircraft carrier built to project power, a threat to the very fundamental basis of the west itself. Why should the world’s second largest economy want to do anything beyond its EEZ?
A question that isn’t relevant for the west it seems.
Call them what the Japanese themselves call them ("Multi purpose destroyers" or "Multi-Role Cruisers" both of which are hilariously made up terminologies), but they're simply not aircraft carriers.
If you really want to do a direct comparison to something in Western militaries, it's basically a LHD/LPD. Something akin to USS Wasp or HMS Albion.
Which, no matter how you want to classify it, is not an aircraft carrier in just about any metric.
Just because a plane can take off from it, does not make it an aircraft carrier. Just like how a vehicle with a gun isn't necessarily a tank.
The rest of your post misses the point entirely. The crux of the problem isn't that "China isn't allowed to build aircraft carriers." There is no moral or legislative restraint (apart from on Japan) that decides which country should or should not build aircraft carriers.
The question that should be asked is, "What purpose does an aircraft carrier serve for the country building it?" followed by, "How should we react to that?"
Let's take for example Italy. It's pretty much the country most invested in the Mediterranean, out of the developed countries. Given that the US 6th Fleet is always chronically under-resourced (mainly because, let's be honest other than some exercises up the Bosphorus and the occasional flair up in North Africa, there's not a lot of the US 6th Fleet to actually do), it makes strategic sense for Italy to have something ready and quickly deployable in case something does happen.
Look at the service history of Cavour. Prior to 2024, it's been to 3 places. USA for training, The Mediterranean sea, and once to Haiti, to provide aid for an earthquake. The strategic onus on this was clear. "We're a backup for the Americans in case something gets rough and they cannot afford to put resources here."
Let's do this for China:
Is it part of a larger, broader naval coalition with standard doctrines to assist? Nope.
Does it have far reaching territories, or pledged alliances? A few, Djibouti, but not really enough to justify large carriers.
What is it's current medium term strategic naval objectives? Break the island chains. Is a carrier useful in this fight? Not really, no.
What about Straits of Malacca and the Indian Ocean? Possibly, but China has land based assets that are accessible and there's also 0 strategic interests there. Well, Straits of Malacca is a strategic interest but you have about 20 land bases accessible to there so again, what's the point of a carrier?
So it makes people think. Why? Why does China need aircraft carriers - especially so quickly and urgently? Also trying to create overmatch with the USA on that field.
Hence, it makes all the countries around it go, "What the feck" in response. And everyone has fully gone, "WTF". When you have little strategic reason to do something, and you start fully committing to it, of course analysts and security apparatuses of other nations are going to try to figure out what the hell you're trying to achieve and react accordingly.
By the way Aircraft Carriers are just one example. Their entire navy composition is just insane for the kind of geostrategic position its in.
When you start building a fleet designed for deep strikes into the Pacific then, well, don't be surprised that everyone assumes you're gearing up to do a deep strike into the Pacific.
India have started doing naval exercises with NATO. France/Italy/Germany have started doing long term naval deployments into the Indo-Pacific. Netherlands are rapidly increasing their surface fleet. The Philippines are buying/building asymmetric area denial platforms. Japan has recently stated it
feels like it needs Nuclear Weapons to ensure its own survival. South Korea in the past half decade has pumped absurd amount of money into its defense industry.
All in all, everyone is hugely alarmed right now with what they perceive to be very very aggressive and maximalist Chinese ambitions.
Sure, outside of some brazen DoD officials, nobody has outright said, "Yeah there's war afoot and we're all going to get wrecked," but it's pretty obvious what everyone is thinking.
Simple analogy:
If Chile started building aircraft carriers - nobody would really care.
If Argentina started building aircraft carriers - people would be incredibly alarmed, especially in Britain.
Its all about the strategic position and what they represent.