I personally think that Childe's first spark of interest began in a similar fashion as it does for any strong character he meets, but there's a key difference in how the relationship evolves.

Based on his first voiceline for Zhongli, which were his thoughts prior to learning Zhongli's true identity, he could already tell that Zhongli was a strong character, and was curious about the full extent of that strength, so I imagine that this hidden strength is just part of what caught Childe's attention. But here's what held that attention.

We learn very, very early on that Childe, for a long time, has grown used to keeping a wall between himself and others. In the Liyue archon quest, after he rescues the Traveler from the Millelith, he eventually says: "Maintaining a distance between strangers is probably a good idea. Either way, I'm already used to it at this stage."

This line is never mentioned or revisited again, but it's the smallest moments of vulnerability—whether it's via his expressions or brief, offhanded comments—that lend nuance to his character and tell us more about his current psychological state. And so with the aforementioned voiceline in mind we can assume that Childe, in the beginning, erected a large wall between himself and Zhongli with the expectation that nothing would break it down...except something did. And as simple as this might sound, the first brick to be knocked out from this wall was due to Childe being treated like a person.

At his core Childe believes himself to be a weapon, as well as a pawn in a larger game. And this core belief has only been substantiated by the events and others in his character arc. Whereas other characters' stories eventually overturn that character's belief and challenge what they thought they knew, Childe's belief has yet to be opposed (the narrative does challenge him to a degree in the Labyrinth Warriors event, but that's for a separate conversation). Since the age of fourteen, he has been continuously used. He has duties, both to his family and to the Tsaritsa, that has required him to smother his own identity in favor of donning a more "pleasant" one, one that meets the expectations of another, whatever those might be. The cold, unflinching soldier and weapon of the Tsaritsa, the friendly and diplomatic "Childe", the responsible big brother and ever successful toy seller—all of these identities are inextricable from himself. They are all, in a sense, him, but the "Ajax" underneath essentially goes unaddressed.

And that's where the wrecking ball comes in.

Zhongli, with his numerous stories to tell thanks to the thousands of years he's lived, is also dubbed "The Listener" and this is also reflected through his behavior. He can often be found at Third Round Knockout, listening to exaggerated, and sometimes even false legendary tales from a past he has already seen for himself. A storyteller, a listener, and a pillar of quiet strength—his personality strikes a balance with Childe's more chaotic inner nature, and he possesses qualities that invoke a sense of safety and familiarity for Childe. Having been raised by a father that told him heroic tales and stories of adventure, Zhongli's vivid stories about Rex Lapis and the Adepti felt like being home, ice fishing and waiting for a fish to bite that might never will.

Along with this sense of being home, Zhongli treats him not like a Harbinger to be feared, but instead like an ordinary person (and this is something they both appreciate in each other, but this is about Childe's POV so I gotta stay on topic). He diligently listens to Childe's mundane stories about his siblings, remembers details that Childe expected him to forget or care little for, and they can lightly tease one another without offense. This is someone who smiles at him despite knowing the archon he serves, who jokes with him, casually invites him to join him for lunch, and looks him directly in the eyes without a trace of fear or hatred. This is someone who treats him like a human.

But not even Childe himself is aware of what separates Zhongli's company from others. It just feels pleasant, warm, natural. It's the most normal, close relationship he has had with anyone in years.

And so that's why I think Zhongli became such a "close associate" (as that Fatuus described Zhongli). It was his strength, his stories, his kindness and attentive nature, his humor and casual treatment that made like Childe feel like a person. And following the knowledge of Zhongli's identity, it is all of these things, plus their similarities Childe had not known before: the burden that comes with being a leader, the life of being a weapon, the struggles that come with being forced to hide your true self underneath a cold mask.

Hope this wasn't too lengthy...I just really enjoy discussing this lol. And I hope I was able to answer your question well!