Did the EU elections show the radical right losing strength or gaining it?

Mattia Zulianello argues that last month's EU parliamentary elections may have shown limited gains and some significant losses for the far-right parties, but they also indicate that their actual influence is still increasing: (Right-wing populist parties made only modest electoral gains in the EP elections, but their influence is now unprecedented EUROPP 05/30/2019):

In conclusion, the modest electoral gains of right-wing populists in the 2019 elections should not be confused with a containment of the relevance of such parties. On the contrary, it is important to recall that right-wing populism performed rather well in the 2014 elections, and that the consolidation of their support across Europe in 2019 suggests centre-right and centre-left parties have limited capacity to develop successful strategies for targeting the electoral base of their populist competitors.

Even when the mainstream moderate parties of the centre-right and centre-left managed to gain votes at the expense of right-wing populists (most notably in Denmark), the former followed a strategy of parroting the policies and narrative frames of the populist radical right, most notably over immigration and asylum. Paradoxically, this has translated into the increasing relevance, influence and legitimation of right-wing populism in European politics.

One of the most notable gains for the radical right was in Italy. The governing coalition there is headed by Prime Minister Luigi Di Maio of the left-populist Five Stars Movement (M5S) with Interior Minister Matteo Salvini's Lega as the junior partner. Di Maio seems to be a weak leader and Salvini seems to be the de facto head of government. The Lega won the most votes of any party with 34% of the vote in the EU election. Angela Giuffrida reports (Salvini's far-right party tops Italy's EU election polls Guardian 05/27/2019):

Mattia Diletti, a politics professor at Rome’s Sapienza University, said Italy had delivered the “most Trumpian” result in Europe. “I knew the League would win, but not by this much, we are now a province of Trumpism,” he said. “Italians were asking for strong feelings and emotion, to feel pride again, and like [Donald] Trump, that’s what Salvini gave.” [my emphasis]

Part of the story of the rise of the far-right parties in Europe during the last decade is the decreasing strength of the center-left social democratic parties, which have been devastated in countries like France and Greece. I haven't seen any election analysis that indicates significant numbers of left/center-left voters switching to the far-right, although it does happen. And there are exceptions to the social-democratic story of decline, for example, in Spain and Portugal and, I would add, Austria. But Germany is a whole different story.

After the SPD's poor showing in the EU elections and in the German state of Bremen, whch followed poor election performances in Bavaria and Hessen, Andrea Nahles is resigning as party leader and also as the head of the SPD caucus in the Bundestag. Andrea Nahles kündigt Rücktritt an Taggesschau 02.06.2019, auf Deutsch):

Germany: Andrea Nahles resigns as SPD leader and parliamentarianDW News In English 06/02/2019:

Declining center-left strength, a fragmenting of votes to smaller parties, stagnation for parties to their left, the far right maintaining its voting power while losing some votes to the center-right parties who adopt xenophobic positions: this adds up to an Overton window shifting in the direction of the authoritarian right. Not a good picture.