Taylor Swift has performed her song “Love Story” hundreds of times since she wrote it nearly 20 years ago. But when she took the stage last month to sing the ballad for a surprise performance at a charity concert hosted by football players, including her fiancé, Travis Kelce, something was different.

It was possibly Ms. Swift’s last time performing the song before marrying her real-life Romeo, as she and Mr. Kelce are expected to tie the knot later this week at Madison Square Garden.

“He knelt to the ground and pulled out a ring,” she sang, wiggling her left hand, the giant diamond on her ring finger sparkling under the stage lights.

Videos of Mr. Kelce beaming from the audience popped up across TikTok. “I love watching him watch her,” one viewer commented. “When your man is your biggest fan,” another wrote.

The Swift-Kelce relationship has some single people pining for partners who will show up for them with unbridled enthusiasm — a man who will broadcast his interest in you on an episode of his podcast before you’ve even met, a woman who will cheer you on from the sidelines and rush onto the field after your big win.

Instead of remaining mysterious and aloof, some singles say they are now seeking partners who are the opposite — or “chalant.”

Chalant — pronounced like its foil, nonchalant — is a made-up word echoing around the internet. In dating, it refers to a state of unabashed excitement and affection, rather than playing hard to get.

“It’s about putting in effort and showing vulnerability, even at the risk of rejection,” said Logan Ury, a behavioral scientist and dating coach who is the director of relationship science for the dating app Hinge.

Chalant dating is a positive shift, Ms. Ury said, “towards people feeling comfortable wearing their passion on their sleeve a bit more and just going after something — and not trying to win that battle of who can care less.”

Some people believe dating chalantly might help them find love faster. Chloe Hannigan, 28, said she aspired to find someone to marry and start a family with. “I just don’t have time to be nonchalant!” said Ms. Hannigan, who lives in Sydney, Australia.

But on social media, there are countless videos of people sharing stories of terrible first dates and dating app fatigue, and some single people have even vowed to take indefinite breaks from dating.

Divine Nmezi, 25, said she would label most men she has dated as nonchalant — “someone that feels like they need to suppress their emotions in order to protect themselves,” as she put it. Ms. Nmezi, who lives in San Francisco, said she had gone out with men who actively pursued her, only to pull back once she showed interest.

Nonchalance often stems from a fear of rejection, experts said. “In a dating world where it feels like no one’s winning, everyone overprotects,” explained Matthew Hussey, a dating expert and author.

For Gen Z in particular, whose every move has been documented online, a fear of being perceived as “cringe” may be partly to blame. A pickup line that doesn’t land can blow up on social media if the person on the receiving end posts about it.

Mr. Hussey said he believes some people are trying to satisfy their needs for romance by idealizing celebrity couples or by getting lost in steamy novels and TV shows. “In any season where we feel like life isn’t offering what we need, we are then prone to escape into these stories where we can scratch that itch,” he said.

These daters are expecting that screen-worthy dynamic in real life instantly, which can lead to disappointment, Mr. Hussey said.

“I think we’ve gotten to a point where we’re treating relationships like Amazon,” said Sabrina Zohar, a dating and relationship coach. “If it’s not immediate at my door, how I want it, then forget it, I’m out.”

But building a valuable partnership takes time and a willingness to be vulnerable, the experts said.

James Oliver, 36, said taking a six-month break from dating and working through his fears of getting hurt had helped him start dating chalantly. “If you can’t handle being rejected yourself, or if you cannot handle respectfully, compassionately and clearly rejecting someone, you shouldn’t be dating,” he said.

Mr. Oliver, who lives in England, has amassed thousands of Instagram followers in the last few months from videos in which he describes his ideal relationship. He also said he had received hundreds of messages from interested women who appreciate his approach to courtship. “I’m speaking about dating to find a wife,” he said. He said he takes the lead on planning most of his dates and enjoys cooking meals for potential partners.

For some daters, that kind of effort and thoughtfulness is more important than lavish outings and gifts, Ms. Ury said. In Ms. Swift’s case, Mr. Kelce tried to hand-deliver a friendship bracelet with his phone number on it to the pop star at an Eras Tour concert he attended.

“It was wild, but it worked,” Ms. Swift later said of the move on an episode of “New Heights,” the podcast Mr. Kelce hosts with his brother, Jason Kelce.

Perhaps someone other than Ms. Swift would have balked at such a public declaration of interest. But for the musician who has been writing love songs since she was a teenager, it was effective.

That’s the benefit of being chalant, Ms. Hannigan said: “The right person would not be turned off by your effort.”