In the movie version, they would have talked for a few minutes and then found an excuse to dismiss their foreign ministers and interpreters. At long last, Vladimir Putin and Donald Trump would be alone and in private. Putin would look the American up and down, as proud as a father gazing upon his grown son. “We did it,” Putin might say softly, almost to himself. “We actually did it.”

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Trump would reply, “It’s your greatest achievement, sir. I am your greatest achievement.” But the time for self-congratulation would be short. Their aides would be back soon. Hurriedly, Putin would give Agent Trump his next set of instructions, then hand him the state-of-the-art microdot camera he would need to photograph the most sensitive documents passing his desk in the Oval Office. Glancing towards the door, Putin would whisper: “Everything you’re doing – the crazy tweets, the attacks on the press – just keep doing it. Every day you’re in the White House, you’re making America weaker. Don’t stop.”

Even the most hardcore anti-Trumpers, those ready to believe the president’s campaign colluded directly with Moscow in corrupting the 2016 US election, don’t think it works quite like that. The notion of Trump as Manchurian Candidate, an agent of the Russian secret service, is fun as fantasy, but it’s no more than that. If there was collusion, it will have involved Trump acolytes rather than the man himself. Besides, any future case against Trump might not have to prove collaboration at all: that Trump sought to impede the FBI’s investigation into the affair, and thereby obstruct justice, would be grounds alone for impeachment.

Yet the assessment by the FBI and others that Russia meddled in the 2016 election – a claim apparently pressed by the US president and denied by the Russian one in their 135-minute meeting – is the prism through which the relationship between Trump and Putin, and between Washington and Moscow, is seen. And, day by day, it is reducing America’s standing in the world.

Consider the almost comic anticipation of the first handshake between the two men at the G20 in Hamburg today. A thicket of cameras watched, as TV anchors channelled their inner David Attenborough, interpreting the body language of the two great apes under surveillance. Who was owning the space, whose posture – Putin sitting back, Trump perched eagerly forward – conveyed dominance, whose suggested submission?

Absurd as such an exercise might seem, even that could not be taken at face value. For what if Trump was only trying to seem curt with a (by his standards) relatively brief handshake, in order to dispel the suggestion that he was Putin’s poodle? True, Trump had tweeted earlier that he intended to “represent our country well and fight for its interests”, but that muscular use of “fight” might all have been for show.

This is where the Russia imbroglio has left Trump. If he had confronted Putin in Hamburg, even fairly neutral observers would have wondered if it was staged for effect; if he’d made a show of comity, then it would be evidence that he was Moscow’s dupe. It did not, for example, escape the notice of the US press that Trump said it was an “honour” to meet Putin (while Putin merely confessed himself “delighted”). That use of “honour” implied a deference that, had Barack Obama voiced it, would not have been forgiven by Trump’s loudest supporters – or indeed by Trump himself. So this is the hole the US president has dug for himself. He can move neither forward nor backward. He is paralysed – and so, therefore, is the US-Russian relationship.

Trump’s weakness, meanwhile, is Putin’s strength. He went to Hamburg knowing the much-ballyhooed encounter with his US counterpart was a “win-win”, as Andrei Kolesnikov, a political analyst at the Carnegie Moscow Centre, put it to the New York Times. If Putin extracted concessions from Trump – whether on Syria, Ukraine or sanctions – he knew Trump would look weak. Equally, if Trump gave him nothing, Putin’s loyal media back home would brand the US president a prisoner of domestic opposition and “Russophobia” – unable to act on his more pro-Moscow instincts. Either way, Trump would emerge as the weaker party.

Remember, few believe that Moscow interfered in the 2016 election because it reckoned it could put Donald Trump in the White House. The more modest goal was to damage the future President Hillary Clinton. US weakness was, and remains, the overriding objective. And on that, the Trump investment is delivering handsomely.

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In every respect, Putin now faces a US leadership feebler than at any time in the 17 years he has ruled Russia – or for many decades, for that matter. It’s not just that both the president and his secretary of state, Rex Tillerson, are foreign policy novices. Or that the State Department is depleted, with hundreds of key posts unfilled. The problem goes much deeper.

The US has lost the moral authority it enjoyed under Obama, a fact visible in the way Trump is treated at international gatherings such as in Hamburg. His break from the Paris climate agreement; his erratic, bellicose behaviour on Twitter; his picking of needless fights with the likes of Sadiq Khan – at a moment when the London mayor’s city was grieving: all have combined to erode what has long been America’s most precious asset – its soft power.

Even in the harder sphere, Trump’s America is a reduced force, simply because of the inconsistency of the man at the top. In his pre-G20 trip to Warsaw, Trump finally gave the pledge many Nato leaders had been waiting to hear: committing the US to Article 5, the one-for-all, all-for-one promise of mutual defence. But Trump has said so many contradictory things on Nato – calling it “obsolete” one day, praising it the next – that who knows what the position will be next week?

On North Korea, it took a 10-minute lecture from China’s president for Trump to realise that that decades-old problem is “not so easy”. Recent days have exposed the US president as having no strategy to deal with a nuclear Pyongyang beyond pressuring Beijing to make it go away. On the Middle East, his gameplan consisted of sending his 36-year-old property developer son-in-law, with no experience of diplomacy or the region, to end a conflict between Israelis and Palestinians that has eluded resolution for the best part of a century. In other words, Putin knows that, in Trump, he is up against an opponent of shockingly low calibre.

Even if Trump had more skill and was surrounded by more able people, he’d still be in a shaky position. His administration is as distracted as he is by the cloud that hangs over them permanently: the gathering investigation into the Russia affair. From Hamburg, Trump tweeted the laughable claim that: “Everyone here is talking about why John Podesta refused to give the [Democratic National Committee] server to the FBI and the CIA”, proof that he obsesses over the details of that saga even when he is meant to be engaged in high diplomacy.

It often used to be said that in the US, foreign policy is domestic policy. That maxim referred to the way US diaspora communities could shape decisions on the countries they had left behind. In the age of Trump, it has new meaning. Thanks to his domestic situation, he can barely move on the world stage. No wonder Putin was smiling in Hamburg. He knows he has succeeded in his chief objective: he has made America weak again.