Outside the White House cabinet room hangs a painting of Donald Trump flanked by Abraham Lincoln and Ronald Reagan, in front of a billowing American flag.

The fan-fiction rendition of three Republican leaders, proudly displayed on a main thoroughfare amid a gallery of other photographs and portraits of Trump, is far from the oddest thing in the home and office of the 47th president. The White House is a homage to gilding and gold, crown moulding daubed in glittering paint, with knick-knacks gaudy and glistening stuffed on to his shelves, a Diet Coke button on his desk, and a new ballroom requiring the partial tear-down of the historic East Wing.

But the painting, spied on the way into Trump’s press conference with Anthony Albanese on Monday, is a good place to start in considering just how much of a political odd couple the two men are – and why, from the outside at least, their remarkably warm first formal sit-down surprised nearly everyone.

Nearly everyone, except the prime minister himself.

Trump, the brash and unflinching authoritarian conservative launching assaults on the judiciary and political opponents to steamroll his agenda, who hangs portraits comparing himself to arguably America’s greatest president who freed the slaves and won the civil war. Albanese, a leftwing warrior turned cautious team captain, who has made a virtue of “orderly government” and knocked more ambitious policies on the head out of pragmatism.

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Walking from the Brady press briefing room, shuffling through poky corridors toward the cabinet room, there was a sense among the media pack that we could be in for – if not a Zelenskyy-style browbeating – at least a disagreement or two. Turning a corner, as if to bluntly contrast the two men, the corridor suddenly filled with wall-to-wall images of Trump.

Trump striding a red carpet in front of Air Force One, Trump brandishing an agreement signed with Israel’s Benjamin Netanyahu, Trump flashing a thumbs up with Palestinian Authority chair Mahmoud Abbas, with giant meme text reading “PEACE 2025” superimposed along the bottom. Right outside the cabinet room, as if to bludgeon your head in with symbolism, a giant oil painting of Trump standing stoically in front of a half-dozen American flags. About 20 paintings and photos, each pumping up Trump’s tyres more than the last, leave visitors in no doubt about whose White House we’re in.

On tables in the anteroom, White House attendants buzzed around preparing for the official lunch to come, plastic bottles of Diet Coke sitting in plastic buckets of ice next to silver platters of crystal ware.

But inside the room, the two men sat side-by-side as partners. Nestled between military flags and nearly needing to shield their eyes from Trump’s gleaming trappings of office, the leaders shared a minerals deal, shared black Texta pens, shared a laugh at Kevin Rudd, then shared a meal.

Albanese famously once said in 2017 that Trump “scares the shit out of me”. It would have been hard for the then shadow minister to imagine he would be sitting in Trump’s White House eight years later, swapping jokes and gifts – let alone to imagine himself praising the Republican president a day after millions rallied across America for the No Kings protests against Trump’s policies, including troubling immigration raids, sending military into Democratic-governed cities, and crackdowns on free speech.

Posters advertising the rally and critical of Trump still hung in streets around the White House the day of Albanese’s arrival. Families and tour groups milled awkwardly on the outskirts of the White House and Capitol building, not allowed in due to the continuing government shutdown as Trump’s Republicans remain in a stalemate with Democrats over budget funding.

Albanese later described his first proper meeting with “very warm” Trump as a major success, the president taking him on a tour of the White House and Oval Office. Albanese and his team had been confident it would go well, the US-Australia relationship – forged in history and the heat of battle – being bigger than the people occupying each nation’s government benches.

The extraordinary warmness shown by Trump was held up as vindication of the prime minister’s foreign policy acumen, and the nerve he had shown in not bending to opposition demands to beg and scrape for a meeting earlier. Sussan Ley walked back her only criticisms of the meeting less than 24 hours after making them, in the face of ridicule for her overreach.

But relief and victory were written across the faces of the PM and his people on Tuesday, realising they had not only escaped the White House without tripping up, but indeed in triumph.

As they fly home on Wednesday, perhaps they’ll be thinking of their wins: Aukus backed in the strongest terms (albeit with mysterious “ambiguities” the US wants to iron out, and which Albanese refused to talk about). A multi-billion minerals deal. Zero blowback from any number of policy areas, from defence to the Middle East, where the two nations have disagreed.

Inevitable criticism from the ALP’s left flank came quickly, with former Labor senator Doug Cameron calling Albanese’s conduct a “capitulation”. Albanese’s joking quip that he would use Trump’s warm words about him in future election ads will be played again and again by progressive critics unhappy about Labor further tying Australia to the US administration.

In 2017, adding to his “scared” remarks, Albanese said: “We have an alliance with the US, we’ve got to deal with him, but that doesn’t mean that you’re uncritical about it.”

At the time, Albanese was a shadow minister. Now as prime minister, he has seemingly worked out a way to deal with Trump – even if they’re unlikely to swap interior design tips anytime soon.