“They have no contact now and she keeps moving forward,” a source tells PEOPLE about the “God Is a Woman” singer, 25, and the Saturday Night Live comedian, 24.

“She seems very happy and positive. She isn’t talking about dating and is instead focused on work and herself,” the source continues.

On Saturday, Grande dropped a new breakup song, “Thank U, Next,” that reviews her past relationships with Davidson, as well as dancer Ricky Alvarez, rapper Big Sean and rapper Mac Miller, who died on Sept. 7 at age 26.

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With a chorus that declares that Grande is “so f—ing grateful for my ex,” the song — which the pop star said shares a title with her upcoming album — offers a self-empowerment mantra: “Plus I met someone else / We havin’ better discussions / I know they say I move on too fast / But this one gon’ last / ‘Cause her name is Ari / And I’m so good with that.”

That same night, Davidson offered kind words about Grande during SNL‘s Weekend Update.

“The last thing I will say is I know some of you are curious about the breakup, but the truth is it’s nobody’s business, and sometimes things just don’t work out, and that’s okay,” he said. “She’s a wonderful, strong person, and I genuinely wish her all the happiness in the world.”

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In an SNL teaser on Thursday, Davidson poked fun at his former engagement. “Hey Maggie, I’m Pete. You wanna get married?” Davidson asked musical guest Maggie Rogers. After Rogers turned him down, Davidson quipped that he was “0-3.”

Grande seemingly fired back at Davidson in since-deleted tweets hours later. “For somebody who claims to hate relevancy u sure love clinging to it huh,” she said.

“Pete’s unfazed,” a source told PEOPLE. “It’s true they’re not in agreement about things after the breakup. A lot of people thought he was the wild card in the relationship, but that’s not true. Pete has and will always joke about his life, with or without her.”

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PEOPLE confirmed that Grande and Davidson were dating in May, shortly after Grande and Miller went their separate ways and Davidson and Cazzie David broke up, and were engaged in June.

“It was way too much too soon,” an insider told PEOPLE in October after the split. “It’s not shocking to anyone.”