This may add a longer pause than is wanted in some situations, like in the middle of what's supposed to be a speech or a breathless ramble. I think sometimes uninterrupted paragraphs of dialogue are warranted.
But otherwise, yeah, action beats with the dialogue is a good tool to have in the box, and to use often.
It's also handy for people who don't want to write "said" all the time, since you can indicate who is speaking with an action beat followed immediately by otherwise unmarked dialogue, or by context alone (e.g. there are only two people in the convo and they're taking turns.) It can add variety to your sentence structures.
Attempted example:
He sat back and sighed. "That's quite a story. But I can't say it's an especially believable one."
"Well," she said, pulling a sheaf of papers out of her purse. "Have a look at this."
He took the papers and shuffled through them slowly, frowning. Halfway through the pile, he paused. Reread something. He looked up and met her eyes.
She held his gaze, then nodded. "I think you can see why this might be a problem for both of us."
It's important that the action means something besides just the pause, imo. You can use actions like that to show something about the character or how they're feeling - like, in OP's example, a character leaning back and looking up like that would imply they are relaxed and casual. If you had them in a different situation or wanted to show a different personality, you might have them do a similar but different thing, like leaning forward and steepling their fingers, or fiddling with a knife (will there be stabbing?!), or taking a slow sip of water, or interrupting themself to make a comment about the food, or clearing their throat. It can be a way to multitask and show something about the character even while they're having a conversation about something else. Whereas not thinking of it as anything but a pause in dialogue might lead to accidentally implying something about the charactee you don't intend to, like making them appear relaxed when they're supposed to be tense, or interested in a conversation when they're supposed to be bored or distracted.