This is a somewhat broad question, but regarding one aspect, there has been some evidence of declaratory shifts towards shelving more immediate EU-exit plans in the platforms of Eurosceptic parties, as noted in a June 2019 Irish Times article:
Five years ago, a core theme of every right-wing populist manifesto was withdrawal from the European Union. Marine Le Pen, the leader of France’s Rassemblement National (formerly the Front National), campaigned on the idea of abandoning the euro and called for “Frexit” at her rallies as recently as 2017. A few years ago, members of Alternative für Deutschland (AfD) voted to include a “Dexit” proposal in its election manifesto. The idea was embraced by the populist right in Italy, Hungary, the Netherlands and across Scandinavia. Getting out of the EU seemed to be one of the main political demands of these parties.
And then, quite suddenly, nearly all of them dropped the idea. Having originally planned to fight the European election on the theme of leaving the EU, Germany’s AfD watered down the proposal in January, and on the eve of the election last month its co-president Alice Weidel remarked that the “Dexit” talk had “clearly weakened” the party. Le Pen still blames the EU for many of France’s ills, but in her party’s latest manifesto both “Frexit” and the idea of scrapping the euro were shelved. “The French people have shown that they remain attached to the single currency,” the document states.
In opposition, Italy’s far-right Lega party made hostility to the EU its USP [unique selling proposition]. Party leader Matteo Salvini held rallies wearing T-shirts that read: “Enough with the Euro”. In the past year, the party has struck a far more pragmatic note. Like Le Pen, Salvini now speaks of finding “common sense” solutions inside the EU. “We don’t want to leave anything; we want to change the rules of the EU from the inside,” he said in December.
The pattern repeats itself across the continent. The Sweden Democrats abandoned its EU exit policy in January. The True Finns party has dropped its call for a referendum on Finland’s membership. In Hungary, the extreme-right Jobbik party, which publicly burned the EU flag a few years ago, no longer calls for withdrawal.
Some political scientists have drawn causal connections with the performance of the Eurosceptic parties in the 2019 electoin and their (open) stance on a EU-exit:
Catherine De Vries, a political scientist at the University of Amsterdam, said her research found that as public opinion became more wary of Brexit, parties started to water down their positions on leaving the bloc.
“It’s not to say they’ve abandoned them but they’ve strategically decided not to highlight them,” she said.
De Vries pointed to the performance of Geert Wilders' far-right Party for Freedom in the recent European parliamentary elections as evidence that campaigning on an 'exit' platform these days is risky business.
The Dutch anti-immigrant party was the only one to explicitly push for 'Nexit' ahead of last month’s elections and were punished accordingly at the polls, she said. (It lost all four of its seats.)
Others (quoted in the same article) were less sure how much of the strength of this change in Eurosceptics' parties stance is due to Brexit alone, pointing to the receding Eurozone crisis as well the taming of the Syria immigration/asylum issue as making the EU look like less of a failure.
It's hard to say whether these effects will last, now that the UK's internal parliamentary divisions are no longer the popcorn of international news... I suppose how the UK's economy will fare in the next year or two will be an important factor in how Eurosceptic parties reposition themselves with the benefit of having observed this "natural experiment".
