There were several competing viewpoints coming from US policymakers on how to proceed in the post-WWII world. It's not so much that the US could do whatever it wished with nuclear weapons (you still need troops to invade countries and bullying your way through diplomacy isn't going to make you any friends), but having them certainly gave it more authority in negotiations. Saying that the "entire world understood [the US] were the de facto military authority in the world" isn't necessarily true. The US certainly did show that it was powerful, especially in the Pacific theatre, but D-Day happened two and a half years after US declared war on Germany—so it's not like US troops could quickly travel to anywhere on the globe. And the Soviets were certainly feared as a military force throughout Europe as they occupied the entirety of Eastern Europe.

Did their foreign policy reflect this attitude?

Somewhat. During the Potsdam Conference in July and August of 1945, President Truman mentioned the existence of a powerful new weapon to Stalin. This is probably the earliest attempt by the US government to use the bomb as leverage in diplomacy. Now, Truman did not make threats towards the Soviet Union of any kind—so don't mistake this for him thinking that US could impose its world order on Europe just by waving around the fact that they created atomic weapons. He probably did so in hopes of gaining some leverage over the ongoing negotiations over Germany and Eastern Europe, but whether this mention was of any help is hard to say.

The bombings of Hiroshima and Nagasaki in August of 1945 are probably the best example of using atomic weapons in an aggressive manner to achieve diplomatic results. If Truman couldn't scare the Soviets by simply telling Stalin about the existence of these bombs, then perhaps a show of their destruction could gain the US some leverage. At this point in the war, the US wanted to avoid a joint occupation of Japan (like what had happened to Germany) and instead wanted to be the sole occupiers of it. Since the Soviets promised to create a Pacific front and were in the process of moving troops to its far east, speeding up the war was certainly in American interests. So, by using the bombs the US could showcase American power and achieve both the surrender of Japan and ensure the Soviets got none of that peace deal. As the Cold War proved later on, once both of the opposing sides manage to get atomic weapons, the actual opportunities to use them decline dramatically. It is probably safe to say that had there been a serious threat of retaliation against the US, these weapons would not be used (or at least would be debated whether or not they should be used much more seriously).

What the atomic bomb did post-WWII is create a "nuclear umbrella" for the allies of the US. It allowed the US to not have to rely on stationing large numbers of troops in places it was interested in, like Western Europe, but would rather scare the Soviets into not pushing their influence into those places by being willing to defend using nuclear weapons.

I looked back over some of the documents for the post-WWII US and Soviet foreign policy, and it seems to me that beyond using the atomic bombs for defense there is little to suggest that the US was able to successfully leverage its monopoly on nuclear weapons to achieve other goals. The monopoly was certainly on the Soviet minds, which is why they sped up their own nuclear program and the monopoly did not last for all that long. I think mostly the US was not able to really successfully leverage its atomic bombs because there were just not all that many of them. Looking at this graph we can see that the race to produce many nuclear bombs really took off beginning in the 50s. The Soviets and the Americans certainly had their disagreements and had acted aggressively countless times, but conventional military forces were still seen as incredibly powerful by both sides.

At that point in time, atomic bombs were still rudimentary devices that had to be carried by planes over the target in order to be used. So during these years, the ability to use the bombs was limited by the strength of the opposing air force and air defenses, as well as the range and speed of American B-29s.

A further short read on atomic diplomacy:

https://history.state.gov/milestones/1945-1952/atomic

Did they act to try to prevent other countries from getting the bomb?

Yes. FDR chose not to disclose that the US had been working to develop nuclear weapons to the Soviets, but he did mention the Manhattan Project to the British. Truman was the one to have told the Soviets about the bombs. And both the Americans and the Soviets tried to gain as many German scientists as they could in the final few months of the war in Europe (Wernher von Braun had famously made his way to surrender to the Americans and would go on to have a great impact through NASA), because both sides knew that Germans had been advancing their knowledge of rocketry and working to create atomic weapons as well. Ultimately though, we know that the Soviets created their own bomb by 1949, so if there were active attempts to prevent others from gaining the bomb after WWII they were unsuccessful.

What leverage did the Soviets have that caused things like the division of Germany?

Occupying half of Europe and half of Germany. Having a large military and being the largest country in the world by area. The Soviets had fought in the war since 1941, took absolutely incredible casualties (the numbers vary depending on your source, but they are staggering regardless) and had the Germans over 1,000 miles into their territory in some parts of the country. Yet they kept fighting on alone on the eastern front and managed to get to Berlin ahead of the Allies.

*Just a personal sidenote, but I believe that the Soviet contributions to WWII are often seriously underappreciated in America. The number of American casualties from all its wars since its founding can be multiplied 3x, and still the number of Soviet soldiers dead or missing in WWII (not even including the wounded like normal casualties) is larger than that. And what the Soviet civilians went through during WWII is just unbelievable in terms of personal sacrifice and their willingness to keep on going.

Did the US want to return to isolationism and not become the enforcer of liberal democracies?

That is a really interesting question. Like I said in the very first sentence of this post, there were certainly arguments made for several paths to be taken in the post-WWII world, and you are right to draw upon earlier US ideas about isolationism. However, during this time there were few strong or particularly vocal supporters of US isolationism. The Soviet Union and communism had overtaken the minds of the American policymakers and citizens as the overwhelming primary threat to American society. And because the Soviet Union was overseas from the US, there was really little question as far as whether America wanted to be the enforcer of democratic ideas by this time. Yes, it did.

Before 1947, the real question was how to best limit the influence of the Soviet Union internationally. The two debates were mainly between whether the US should act aggressively to contain the USSR or whether it should try to cooperate and work with the Soviet Union. By 1947, it was clear that both sides decided to act aggressively to protect the already established spheres of influence. In the case of the United States, the Truman Doctrine, the Berlin Airlift, the formation of NATO, the Marshall Plan, and issuing a peacetime draft in 1948 are examples of aggressive US foreign policy that acted on American international interests.

In the 1948 election—when the Chicago Daily Tribune famously jumped the gun on declaring the winner of the election—both the Democratic (Truman) and Republican (Dewey) candidates agreed on an aggressive foreign policy, which left little doubt as to the improbable return to isolationism. And the Truman Doctrine and the Marshall Plan had plenty of bi-partisan support in Congress to allow President Truman to fully enact his foreign policy.

Sources:

U.S. Diplomacy Since 1900 by Robert D. Schulzinger, 6th edition.

America in the World: A History in Documents from the War with Spain to the War on Terror by by Jeffrey A. Engel,‎ Mark Atwood Lawrence, and‎ Andrew Preston.