As a two-term Democratic mayor of New York City, Bill de Blasio earned mixed reviews, at best. But now that he’s out office, he’s getting raves for the way he is handling an unexpected development: his separation from his wife and the transformation of their marriage.

Last week, Mr. de Blasio and his wife, Chirlane McCray, announced in The Times that they were going to start dating other people, while still living together in their Park Slope rowhouse. It was an unexpected moment of both transparency and ambiguity that transfixed many New Yorkers. The couple did not plan to divorce, they said, though they didn’t rule it out. One of them may move out eventually, or not. They left that open.

In a world accustomed to the sight of angry divorce implosions, marriage therapists, advice columnists and regular New Yorkers saw it as both refreshing and groundbreaking for a political couple to be talking about their separation with so much mutual respect.

Their desire to not see marriage in strictly binary terms — as either monogamy or divorce — was also both very of the moment and as old as marriage itself, relationship experts said. And it was, in its emotional risk-taking, somehow very New York.

In New York, “I think we are on the forefront of different experimentations in general,” said Irina Firstein, a couples therapist in midtown Manhattan.

“We’re kind of more honest, more gutsy, more aggressive. We deal with a lot of stress,” she added. “So I think there’s a certain type of mental, emotional, social, and sexual flexibility that comes with that.”

With housing prices sky high and custody issues often influenced by who remains with the children, the decision to keep living together after a breakup in New York is often less about openness to new relationship formats, and more about the financial and practical matters. Some New Yorkers who have been through it spoke about how emotionally brutal it can be if not handled well.

Deen Cameron, 31, a software engineer and a Brooklynite originally from Ohio, said the couple’s announcement could lead to a “really beautiful thing to not have to leave someone’s life, that you were with.” But Mx. Cameron, who uses they/them pronouns, also recalled the experience of living with an ex for a time in their home state as “awkward” and “sad.”

Officially, Mr. de Blasio, 62, and Ms. McCray, 68, labeled their new arrangement a trial separation, which typically means a couple tries to live apart for a while, with a hope of salvaging the marriage and its intimacy for the longer term. This, several experts said, did not seem like that.

“If you’ve already decided you’re going to date other people, that doesn’t sound like your intent is for you to reconnect and be intimate with one another,” said Marlene F. Watson, a couples therapist and the director of training at the Ackerman Institute for the Family in Manhattan.

And yet, it was evident that they were trying to preserve many aspects of their 29-year marriage (their finances, their shared family with their two grown children, their friendship) even though they knew something — the “lovey-dovey” feeling, in Mr. de Blasio’s words — was missing.

Dan Savage, the author and sex advice columnist, said the couple’s description of what their arrangement may become sounded something like his own personal situation. He practices a type of hierarchical polyamory, in which he and his husband of nearly 30 years each have a long-term boyfriend, while keeping their marriage bond primary.

“They’re kind of publicly acknowledging something that most people can barely bring themselves to admit, which is that three decades into a marriage, almost all marriages at that point are companionate,” he said.

“What they want is N.R.E., as the poly people call it — new relationship energy, the excitement and lovey dovey-ness that characterizes a new relationship,” he added. “But they don’t want to lose the bond they share.”

Orna Guralnik, a clinical psychologist and the star of the Showtime show “Couples Therapy,” also saw something very contemporary in their decision, and reflective of what she is seeing in her younger clients.

“It is common in Brooklyn and common in New York in terms of how people are reimagining what family structure is about,” she said. “There are just so many more options nowadays.”

And yet, married couples for millenniums have found ways to find satisfaction beyond the marriage while staying together, if not always in ways that were equal to both partners.

Ms. Watson, a Black woman, said the arrangement reminded her of what she saw growing up in segregated communities in the 1950s and 1960s in Virginia and Pennsylvania, when couples who were no longer intimate would often remain married but carve out separate lives.

“I don’t think we really invent new things in terms of relationships,” she said. “But I think that Bill and Chirlane ought to be commended for being honest and upfront about what they’re doing.”

Katherine Woodward Thomas, the Berkeley-based family therapist who coined the term “conscious uncoupling” more than a decade ago, said that the key to making the next stage work would be honesty, as well as clear communication about the situation with their two children, who are in their 20s.

That will be true, she and other experts said, no matter how this turns out — whether one person falls in love and ultimately wants a divorce, or if they find a way to have a more open relationship.

The first step down a long road of untangling the emotional bonds of marriage will be to build a fuller identity outside of politics and the home, Ms. Thomas said. And that may well be harder for Mr. de Blasio than Ms. McCray, who had a proud personal identity as an out lesbian before marrying her spouse.

“He needs to go out now and to develop himself — and not just on the dating scene,” Ms. Thomas said. “He’s got a big makeover ahead of him.”

The biggest cultural contribution their separation story could make, Mr. Savage said, would be sparking a conversation for other couples who, after decades together, seek respectful ways to value their marriages while opening the door to something new.

A few blocks from Mr. de Blasio’s YMCA, neighborhood residents generally had good things to say about his and Ms. McCray’s announcement. Some commented on how “Brooklyn” it was and thought it could set an example for other couples in similar situations.

“It’s inspiring what they’re doing,” said Kent McVey, 65, while on a walk in Park Slope with his wife of 43 years, Laura, 67, and their two dogs.

“To me, that just shows that there is a deep, deep level of respect and friendship,” he said. “If they don’t stay together and they end up dating other people and they marry someone else, they’re going to stay friends forever. What other way would you want it? I think that’s incredible. I love it.”

Olivia Bensimon contributed reporting.