Joe Biden's surprise visit to Ukraine on Monday is a striking show of solidarity - an intentionally powerful message to Moscow - as Kyiv prepares to mark the grim and bloody one-year anniversary of Russia's invasion.

Ukraine's government was understandably thrilled to see the US president but - as a professional Europe-watcher - one comment stood out for me in particular.

Deputy Foreign Minister Andriy Melnyk celebrated what he described as "the presence of our important, main partner."

Shouldn't that be Europe?

Vladimir Putin's aggressive ambition is a threat to European security first and foremost. His invasion of Ukraine has brought conventional warfare back to this continent on a scale not seen since World War Two.

His actions have shattered the sense of peace and relative security most of us were used to. For the first time since the Cold War, the possibility of a nuclear attack is being discussed as a real possibility - however remote.

But Europe - in and outside the EU - is a sum of many and diverse parts.

Russia's invasion has been a clear reminder to Europeans - even France's President Macron, the normally outspoken advocate of Europe's "strategic autonomy" - that, in terms of defence - the continent can't go it alone. The money, the military and weaponry, the united resolve isn't there compared to the US (and even there, some tiny political fractures are beginning to show).

That said, the Kremlin underestimated Europeans a year ago.

It bet on them being weak and wholly divided, with each country looking out only for its short-term benefits (like stable energy prices). And the United States being distracted by China. Vladimir Putin underestimated leaders' resolve to stand by Ukraine and their version of European stability.

Russia's invasion of Ukraine changed Europe.

Countries have come together - some slower, or more reluctantly than others - but still: with unprecedented sanctions against Russia. Western allies' initial red lines have been repeatedly broken as they've clubbed together to send increasingly powerful weaponry to help Ukraine.

As the war now approaches its second year, that unity - however imperfect - still holds. Though flickers of public dissent are appearing, for a number of reasons.

Take European big power Germany.

The Markus church in Berlin's Steglitz neighbourhood was packed when I visited recently.

Refugees sat side-by-side with German locals as the hauntingly beautiful voices of a Ukrainian mother and daughter singing traditional songs floated out into the freezing night.

Though Europe's biggest economy has conspicuously failed to play a leading role in the Ukraine crisis, Germans call the war their "watershed moment". They opened their arms to around a million refugees and transformed post-war defence policies to help Kyiv.

Along with other European allies, Germany's leaders agreed to send heavy weapons, missile launchers and most recently its prestigious Leopard 2 tanks to help Ukraine fight off Russia's invading forces.

But the sentiment of solidarity is slipping a bit. And not only in Germany.

In stark contrast to the proclamations of Europe's political leaders, 48% of the public want a quick end to hostilities, even if that means Ukraine having to hand over some of its territory to Russia.

That was the finding of an end-of-2022 survey published by research group Euroskopia, based on questions put to a total of 9,000 people in nine EU countries.

This doesn't mean almost one in every two Europeans is preparing to turn their back on Ukraine. As the BBC's Europe editor, I travel regularly around the continent. Wherever I go, people tell me they want the suffering there to stop.

But as the war grinds bloodily on, views differ sharply over how much they want their country to still be involved, at what cost to them, their family or their businesses (think about spiralling energy costs) or the risk some analysts talk about of the war "escalating" beyond Ukraine, perhaps even involving nuclear attacks, and also to what extent they think Russia should be pushed back or punished.

War-weariness is certainly something that Ukrainians are increasingly having to contend with - whether they are refugees looking for lodgings or politicians in Kyiv trying to drum up more military support.

"One month, two months, three months… I was with a German family for eight months!" Nina from Kharkiv told me, as I sat with her, towards the back of the Berlin church.

"They were like real family. Wonderful. And they didn't actually ask me to leave. But I knew it was not good. Guests are great but not for so long. We don't know when this war will end."

Donations for refugees have plummeted an eye-watering 95% since the start of the conflict, according to church chaplain Sven Grebenstein.

More than fatigue with the Ukraine war, he thinks Germans have been distracted by the impact of the cost-of-living crisis, linked to the conflict.

"[Germans] were falling over themselves to help 12 months ago. They were generous with their time and their money. But then they saw their bills - gas, electricity and food - shoot up. They started being more careful with money they might need for themselves."

Italy, like Germany, used to be hugely reliant on Russian gas, before the EU slapped sanctions on Moscow following its invasion of Ukraine. The energy crisis hit hard.

Half of Italians don't want to send any more weapons to Ukraine, according to opinion polls. Only 26% say they support more sanctions against Russia, if they'd make life more expensive. The same study suggests the percentage in France is 27%.

This is a world away from the strongly pro-Nato, pro-military aid stance taken by Prime Minister Giorgia Meloni or President Macron. You can't help wondering if that gap between leaders and so many voters is sustainable.

Suspicion of the US and Nato and an openness to the Russian narrative is something you often come across in Italy.

Murano, near Venice, is famous for the eye-catching, centuries-old artisanal skill of glass blowing.

To create stunning, mouth-moulded vases, stools, bowls and even chandeliers, the glass needs to be molten. Furnaces are kept at a constant temperature of 1200-1400C.

The industry has been decimated by spiralling energy bills. But when I visited the Wave Murano Glass factory, I found many workers unwilling to blame Moscow.

Young Gabriele told me he didn't want to compare his family's suffering to that of civilians in Ukraine but, he insisted, the war had claimed victims all over the place. The cost-of-living crisis is very real for him and his elderly parents living on a basic state pension. He wasn't an expert on politics, on who's right and who's wrong but, he said, the war needed to stop.

Factory founder Roberto Beltrami told me Italian attitudes were also affected by the fact that so many businesses had traditionally strong links to Russia.

Moscow is well aware of this. Italy and Germany are big targets of Russian disinformation campaigns.

Travel 2,000km to the north-east and, in the Baltic states, you find a completely different European picture.

Losing business and investment here is in no way viewed as an obstacle to a tough line against Moscow and public opinion is overwhelmingly in favour of strong support of Ukraine. Tiny Estonia spends more than 1% of its GDP on military aid to Kyiv.

The Baltics are viewed as some of Europe's most "hawkish", or hardline nations when it comes to dealing with Russia. Poland and the UK have a similar profile, with the Netherlands not far off.

Estonian Defence Minister Hanno Pevkur told me Russia's invasion on 24 February 2022 resonated here in particular, as it coincided with Estonia's independence day.

Estonia, Latvia and Lithuania were occupied for almost 50 years before the collapse of the Soviet Union. Geographical neighbours of Russia, they've lived in permanent fear of being invaded again.

Members of the EU and Nato, they're relieved other Western countries now see Russia as a strategic threat to all of Europe, rather than dismissing as a "regional issue" the Kremlin's designs on Ukraine and potentially reasserting its influence over other neighbours.

Ambassador Christoph Heusgen, who chaired the weekend's annual Munich Security Conference, used to be a key adviser to German ex-chancellor Angela Merkel. She's now blamed by many for having harnessed her country far too closely to Russia.

When I asked him if he now felt he had been short-sighted, he insisted Germany's relationship with Russia was hugely complex. You need only remember the 20 million people slaughtered by the Nazis on lands then belonging to the former Soviet Union. But he conceded that the perspective of Western European leaders on Russia had now definitely changed.

"They recognise this is an attack on Europe. This is an overall attack on the European security architecture," he told me. "I personally believe, and I think many do, that if Putin would be able to conquer Ukraine, he wouldn't stop there. He would continue to... reinvigorate and re-establish the Soviet Union in all those territories that he believes Russia lost. Moldova is talked about. But I think also he has put his eyes on the Baltic countries."

It's for this reason the EU is now turning its attention, though critics argue not enough, to Moldova and Georgia. Even to Armenia and Azerbaijan.

And it's why the Baltics describe themselves as Europe's front door. They've long called on the West to bolster them in order to protect the continent from an aggressively ambitious Russia.

In the snowy wilds of the dense pine forests outside Tallinn, the Estonian capital, I saw for myself how Nato had paid attention.

Its presence in the region has been massively increased. A huge military exercise was under way, complete with tanks, Chinook helicopters and trench warfare.

The multinational troops I spoke to - from France, the UK, Denmark and of course Estonia - were clear why they were there.

"I'm proud to defend Europe," Julien, a young French lieutenant, said smilingly.

"We are one," declared Bernadita, a military planning officer from Copenhagen. "And an attack against one of us is an attack against all."

But public disengagement we're seeing in pockets of Europe must give pause for thought.

And after the conflict finally ends?

Never mind a divided public, there's no unity even among Europe's leaders as to how to deal with Russia.

Isolate or try to re-integrate, based on the premise that the future security of Europe cannot be meaningfully discussed without Moscow somehow being included? These questions are looming but as yet, unanswered.