“The E.U. is sick of this,” said Nathalie Tocci, director of the Rome-based Institute for International Affairs and an adviser to the bloc’s foreign policy chief. “But the E.U. is not the problematic side. They were firm and consistent, and ultimately the E.U. got its way in the way it had foreseen.” That meant forcing Britain to choose whether to keep the entire country in the customs union, as former Prime Minister Theresa May chose, or just Northern Ireland, as Mr. Johnson did.

Of course there are serious concerns that Mr. Johnson might fail to win approval for this withdrawal agreement on Saturday in the British Parliament, much as Mrs. May failed to win approval for her deal three times. “But despite their anxieties of ‘Here we go again,’ the E.U. was willing to try,” said Rosa Balfour, an analyst in Brussels with the German Marshall Fund. “They don’t want to be seen to be pulling the plug.”

If Mr. Johnson fails in Parliament and must request an extension beyond Oct. 31, as his Parliament has legislated, the European Union will provide one, Ms. Balfour said, presumably for a new election in Britain.

Even if Mr. Johnson succeeds, European leaders worry that he is not sincere about negotiating a future trade agreement that hinders him from cutting British corporate taxes and regulations. They fear he will turn Britain into what Chancellor Angela Merkel of Germany has called another competitor with the bloc, but one that is right next door.

But it is crucial now that the European Union move beyond Brexit to face a complicated world, said Enrico Letta, the dean of the Paris School of International Affairs and a former prime minister of Italy. Thursday’s summit was supposed to be devoted to finding an agreement on the bloc’s next budget and deciding whether to open negotiations with North Macedonia and Albania about joining the bloc, he said. The Syria crisis is important now, and “there needs to be a strong European position,” he said, especially when Vice President Mike Pence is in Ankara, the Turkish capital.

Migration issues are unresolved, and the new European Commission has been delayed in taking office by battles within the European Parliament, Mr. Letta said. “The risk is to focus everything on Brexit and lose focus on everything else.”