Interesting article, thanks for sharing.
Upon reading, I came across some statements that I'd like to improve or alter, if it was me writing the text.
Each successive world system has a leading state
Here, I would say: there can be many. Multiple centers of power can exist and persist for long periods of time.
After World War II, the US took over from the UK and became the architect of the next world system, centered around a putatively universal order of states governed by the UN
The author has mis-stated the nature of the UN - it has no capability to govern. It's a sofa corner where states chat through their delegates - and proceed to do what they really want. Only a small state takes a resolution of the UN seriously.
The US and its closest allies are no longer the main motors of economic growth, and the share of new investments they capture is diminishing.
Almost correct. China is on equal footing in terms of economic output, and still growing faster -> thus, likely to surpass the US. However, the "US and its closest allies" is a term that makes further comparison impossible - it could be right or wrong depending on how one charts alliances.
Politically, the NATO bloc had been expanding its web of alliances into territory that had long belonged in the Russian sphere of influence. Russia is pushing back in Ukraine
This sentence irritates me - a lot. Countries aren't forced to join NATO, they choose to join NATO - Finland joined last year, Sweden will join this year, most of Eastern Europe joined when they could. Ukraine never joined and never seriously had a chance before the Russian invasion.
Russia's "push-back" in Ukraine however, is not something Ukraine chose - it's a full-scale war. NATO didn't get Poland or Hungary or Estonia to join by waging a full-scale war against them. They just left the door open - the countries applied, nobody vetoed, they became members. A direct comparison between NATO expansion and Russia's actions in Ukraine on such simple terms is highly inadequate, unless one's trying to fool the reader.
divisions within NATO and the EU have recently immobilized those alliances
That would be false. The EU recently passed its 50 billion euros of aid to Ukraine. Member states continue to send armaments. Finland shipped its 22-nd armaments package to Ukraine, the Netherlands and Denmark have probably already handed over F-16 fighters (there have been photos of an F-16 in Ukrainian colors). France continues to supply artillery to Ukraine, Germany continues to supply air defense. Greece is negotiating the handing over of Soviet-made weapons. Bulgaria is supplying considerable amounts of ammunition and also giving away its Soviet-made war machines.
The sore thumb at the moment is the US - for several months in a row, the parliament of the US has been deadlocked, and 90% of the blame seems to be on Trumpist Republicans. About 60 billion of aid stands behind the deadlock - about as much as the EU gave, but this package of aid has higher percentage of critcally important weapons. Thus the fuss.
Elsewhere, Russia has suffered humiliating defeats, as in its inability to support Armenia against the expansionism of Azerbaijan
I would agree with this assessment, but I'd note that both Armenian and Azerbaijan are allies of Russia. It was supposed to mediate between them - in more direct terms, to play them against each other so they can be ruled over - but it failed due to being drawn out in Ukraine.
Turkey is acting on a strategic level like a non-aligned country, even as it continues to wield the ability to block consensus within NATO
Yes, it behaves like on. However, the blocking of Sweden's NATO accession was overcome by US foreign policy - Turkey needed weapons systems which the Congress would not permit giving, unless Turkey would permit Sweden to join NATO. So recently, Turkey ratified the deal (Hungary still blocks at the moment).
In the US, the political elite already consider China an adversary worthy of a new Cold War, whereas in Europe, China is considered a partially reliable strategic partner. If something does not change quickly, the US will be relegated to the same status.
This assessment seems accurate, but I'd like to quote the EU on this. Their position is more complex:
"The EU sees China as a partner for cooperation, an economic competitor and a systemic rival" -- EU-China Relations factsheet
the US would need to make grand gestures in order to expiate their rotten brand: /.../ normalizing relations with China and Iran
Iran is actively supplying armaments to Russia for its war in Ukraine. China meanwhile has not excluded conducting a violent invasion of Taiwan, and drills their military for this course of action on regular basis. How does one normalize relations with an ally of an agressor, or a party preparing for agression?
...I actually liked the rest of the article.
P.S. As for legitimacy: yes, there are horrors in the behaviour of past US administrations. States get away with violating international law if they are powerful enough. :( The US has done to South America what the USSR did to Hungary, Czechoslovakia, Afghanistan and various places it occupied. The USSR has crumbled (apparently, one of its successor states has the same habits). The US - has it reformed itself? I can only say "maybe", "hopefully" but there's no certainty. The system doesn't look particularly different, people might have higher awareness and standards but the sprockets and wheels are the same.