Ah yes, the "source?" argument. The classic cry of people who want to disagree but have nothing productive to add to the discussion.
I could point you to literally dozens of books on the Pax Americana and its decline (google is your friend) and America's de facto empire, as well as historical studies of the Pax Brittanica and the Pax Romana. Or Chinese histories that discuss the waves of peace and prosperity following the growth of major dynasties which end exactly the same way. I suspect you won't read any of them though, since nobody who asks for a source in an online discussion really wants a source (nobody ever asks for a source when they agree with you). They just want to claim that their counterpart is uninformed.
You want to engage in a debate involving cited sources? What's good for the goose is good for the gander - write a response with a citation or two that rebuts a key point. Otherwise, asking for sources in online arguments is borderline trolling.
Look. You made the claim; you have the burden of proof. What can be claimed without evidence can be disbelieved without evidence.
But also, on an online forum, a post is written once, but read many times. When you say "look it up yourself", that doesn't tell one person to look it up, it tells 10 or 100. That's inefficient - the looking up is done multiple times rather than once.
And, I can google for why the earth is flat and find plenty of resources. The fact that I can find stuff on google that supports your position doesn't say much.
So, yeah. Maybe you could supply some resources that you think are solid, and why you think they are?
The problem with narrativized framings like "Pax Americana" is that they only work if you focus on internal peace. The "American" century began with World War 2 (arguably) and was defined by continuous proxy wars and assassinations. The US also didn't stand unchallenged at least until the decline of the Soviet Union (remember: the commies even won the "Space Race" before the goalposts moved to putting a man on the moon) but arguably that was also a crucial step in the rise of China as a direct challenger.
In the case of Pax Americana the framing is also dubious as it wasn't American dominance that kept the peace in Europe (on this side of the iron curtain) but arguably more the shared market and the necessity of cooperation to recover from the wounds of two world wars while facing the threat of annihilation in the conflict between the US and the Soviet Union.
Even in Europe this period was heavily defined by oppressive policing in both East and West Germany (culminating in the fall of the Berlin Wall in the East and the student protests and RAF terrorist attacks in the West), civil war in Northern Ireland (with terrorist attacks reaching deep into England at times), separatist movements in the Basque region, the excruciatingly slow death of fascism in Spain and Portugal, the violent suppression of striking miners in the UK, and the birth pains of neoliberalism and austerity.
The "pax" in these titles always only applies in a very narrow sense to the affluent in its imperial core, i.e. the American upper middle class of the 1950s or the British bourgeoisie of the colonial era. Even the Pax Romana is not a coherent description of life in the Roman Empire for the time frame it is often applied to and was defined by expansion (i.e. military conquest) not an absence of war.
If anything, the "prosperity" these terms often imply always only existed because of a hierarchical system of exploitation and the "peace" refers to the absence of serious challengers to disrupt this exploitation. The prosperity in Britain during the Pax Britannica specifically only existed due to the violent oppression of British colonies and the absence of powerful challengers to claim those colonies instead. Following the war economies of WW2, the 20th century saw a massive redistribution of wealth and public infrastructure to the financial elites, especially under Reagan in the US and Thatcher in the UK, while colonialism largely evolved from the crude brutal oppression of e.g. the British Raj to loans and privatization, aka "soft power" (promoting the production of worthless cash crops for international trade at low margins instead of vital food crops, making the economy dependent on imports to keep the local population fed, or exporting raw resources rather than building up local infrastructure to refine those resources into goods that can be sold at a higher price and thus having to import the finished goods at exorbitant prices).
So, yes, for you or I living in the imperial core - whether literally in the US or by extension in Europe - the "decline" and the rise of challengers is worrisome and can only be negative. But ultimately, especially to those living outside that core, the challengers are no worse or better than the status quo.
Yes, I agree with you that the "peace" mostly applies to those in the fold, and the only people who enjoyed a real, enduring peace for the whole time are the middle and upper classes of the very core of the empire. Personally, I would suggest that much of NATO (but not all of it at all times) has had relative peace during this time. The borders of empires have always had belligerents that need "putting down" from the perspective of the empire, which means small proxy wars. However, the "peace" usually refers to wars between nation-states.
Much of Europe's economic policy benefits from the huge subisdy that the US covers them with its guns - a drain of 6-10% of GDP may otherwise apply to NATO countries that find themselves up against Putin (and in a hypothetical world - maybe against each other). The Marshall Plan is also a relatively visible indication of how intertwined Europe's post-WWII growth was done with America's involvement, and when you look at US foreign aid ("imperial economic stimulus"), a lot of it today goes to poorer European nations. I agree with you that the EU (post-iron-curtain project) has been, as you suggest, a solely European initiative driven more by European solidarity than US guns. However, it exists in the world of the petrodollar (not any more) and with the quiet reassurance that many of the leading nations in the EU are NATO members. As we have seen with Ukraine, sometimes that NATO membership matters.
Empires are always a lot looser than we think - the Roman empire was a great example of this, where the nation-state of Rome (in the modern idea) didn't extend beyond the Alps until the Caracalla years, where Roman citizenship was truly extended to the provinces (note: after the end of the pax Romana). Egypt and the levant were basically completely autonomous, much like the EU is today.
What you call "policing" they call "exploiting". Every single country that has dared to vote too left wing has had CIA or USA army having something to say about it.
This happened in europe, south america, and middle east.
> I suspect you won't read any of them though
That's very unacademic of you to suspect I won't read "the books", which you didn't even bother to list.
I could point you to literally dozens of books on the Pax Americana and its decline (google is your friend) and America's de facto empire, as well as historical studies of the Pax Brittanica and the Pax Romana. Or Chinese histories that discuss the waves of peace and prosperity following the growth of major dynasties which end exactly the same way. I suspect you won't read any of them though, since nobody who asks for a source in an online discussion really wants a source (nobody ever asks for a source when they agree with you). They just want to claim that their counterpart is uninformed.