What is the word or phrase to describe the action of pursing one's lips in a tight rounded shape in a happy mood?

As the title says, what is the word or phrase to describe the action of pursing one's lips in a tight rounded shape in a happy mood?

Merriam-Webster: purse(verb) defines it as (quoting from English Language Learners):

to form (your lips) into a tight circle or line

So "purse one's lips" can mean forming a line instead of a circle.

Cambridge Dictionary: purse(verb) defines it as follows:

to bring your lips tightly together so that they form a rounded shape, usually as an expression of disapproval

Example: "I don't approve of that kind of language," she said, pursing her lips.

So "purse one's lips" usually shows the feeling of disapproval (although I think it can also mean a happy mood).

But I'm trying to find a word or a phrase that specifically refers to "rounded shape" and "happy mood". For example, "So happy to see her boyfriend again, she ___ her lips to ask for a kiss from him." From our life experience we know that, in this example, when she "___" her lips, the lips don't form a line but a circle, and she must be in a happy mood.

I'm aware of this question What does the phrase "to purse your lips" mean？ [closed] but it doesn't answer my question.

Pucker

to tighten skin or cloth until small folds appear or (of skin or cloth) to form small folds

He puckered his lips and kissed her.

[Cambridge Dictionary]

Pucker is a verb for what happens when something smooth or flat gets folded up into little wrinkles, like how you pucker your lips when you go to kiss someone — you, wild flirt, you!

[Vocabulary.com]