Katya Adler: Jubilation in Budapest will be felt in Europe but leaves Moscow cold

"I cried when I put the X on my ballot paper," Zsofia told me. "I still can't quite believe we did it. But we did!"As Zsofia spoke, her group of friends were loudly chanting "Russians Go home!"Marianne Baisnée / BBCThere was a definite sense in Budapest of history being made on Sunday nightIt's an ironic full circle for Orbán. He became famous in 1989 in then-communist Hungary, calling on Russians to go home in a passionate speech he gave in the dying days of the Soviet Union. It's a phrase that first ricocheted through Budapest during Hungary's ill-fated anti-communist uprising of 1956.But over the years, Orbán changed his political stripes. He moved further to the right, adopting an authoritarian edge, and throughout this election campaign, that slogan of his youth was thrown back in his face by critics, outraged by his longstanding, cosy relationship with Russian President Vladimir Putin. Orbán's ousting is a real blow for Putin, who benefitted from having an ally inside the EU. Orbán delayed sanction packages after Russia's full-scale invasion of Ukraine and has been blocking a huge EU loan to Kyiv it says it needs to survive.But Russia's loss is Ukraine's gain. President Volodymyr Zelenksy was quick to congratulate Magyar on Sunday night, writing on X that he looked forward to "constructive work" together.Marianne Baisnée / BBCFidesz plastered posters of Magyar and Zelensky, trying to link the two leadersNot exactly effusive, you might think. But Zelensky is acutely aware that many Hungarians are wary of his home country. Orbán used campaign posters and rallies to warn voters that only he could keep them safe and prevent the war in Ukraine seeping across the border, endangering the lives of their loved ones.Magyar will probably tread carefully once in government. He is unlikely to reverse Orbán's decision not to send military aid to Ukraine, for fear of alienating Hungarians, though he has promised Brussels that his country will no longer obstruct the Orbán-blocked €90bn (£79bn; $105bn) loan to Kyiv.Few European leaders will shed a tear at Orbán's departure. In Brussels he was nicknamed "the Obstructor" but more broadly he was viewed as the faultline in a European united front when it came to threats from Moscow, Beijing and, more recently, the US too.On Sunday night, UK Prime Minister Sir Keir Starmer described this as a historic moment for European democracy. The European Commission President Ursula von der Leyen said Hungary had chosen Europe.ReutersUS Vice-President JD Vance joined Orbán on stage during an event in Budapest the week before the electionOver in Washington, US President Donald Trump will have been distinctly less cockahoop. Hungary's voters have robbed him of his closest ally in Europe. He repeatedly endorsed Orbán, even sending his vice-president to Budapest in the middle of the Iran war to appear at a pro-Orbán rally. Why? Both men admire the outgoing Hungarian prime minister as a leading figure of the Christian nationalist, "anti-globalist" right. Steve Bannon, the former chief Trump strategist and champion of populist nationalist movements in Europe, described Orbán as a "hero".While some analysts tout Orbán's ignominious fate as a sign that populist nationalism in Europe has reached a plateau, I am wary of drawing those conclusions. It's true that Marine Le Pen's National Rally party underperformed expectations in French local elections last month and that Italy's Prime Minister Giorgia Meloni was recently punished by voters in a referendum on judicial reforms that became a judgement on her premiership - but these examples all prickle with national peculiarities.Orbán had long-alienated sections of Hungarian society: the left, the LGBTQ+ community, many women who felt their rights were being eroded with the Orbán "pro family, pro traditional gender roles" agenda. But the final nail in his political coffin came when even core Orbán supporters abandoned him in their droves.Marianne Baisnée / BBCThe BBC visited Orbán's home village of Felcsút the day before the electionA day before the vote, we visited Orbán's home village, Felcsút. Once from a humble background, he has now poured money into the community here, building his own football stadium and football academy. His son-in-law is linked to a luxury golf course in the area, while his father is rebuilding a nearby private estate, said to cost around $30m (£22m).Orbán has always denied corruption allegations and, when Hungary's economy was healthier, many here were willing to more or less turn a blind eye. But in recent years, inflation has soared and standards of living sunk, while Orbán's close circle seemed to be getting ever-richer."He failed us. He failed his country. He hoodwinked us," Gyárfás Oláh, a former Orbán enthusiast and ex-local mayor, told me wearily.Amongst Magyar's voters are significant numbers of Hungarians who voted against Orbán rather than for Magyar himself. He's not yet tried-and-tested in government.So who is he? What kind of prime minister will he be at home, or as an interlocutor for Hungary's allies abroad?Well, he's an energetic (on the campaign trail he appeared at four to six rallies a day), smart and telegenic 45-year-old, formerly from Orbán's party Fidesz. This means that, like Orbán, he's a conservative nationalist. He loves to carry a Hungarian flag with him to any and every political event.Arguably Hungarian voters needed a centre-right candidate to unite around before they considered turning their back on Orbán. Hungary is a socially conservative country. You can expect Orbán's anti-migration attitudes to continue under the new government, for example.Magyar has, though, promised sweeping reforms "to roll back the Orbán regime", including weakening ties with Russia and rebuilding bridges with Europe.For now, most Hungarians say their priorities are domestic: improving their country's sagging economy and public services, lowering inflation and the cost of living. There's a lot to do.