It's even more interesting how, even when the camera was afar, his head kept turning. I noticed that from an animation standpoint, this was indeed intentionally done, possibly to portray his character. Why? I don't know, but I have a few theories:

It might have been done to make him appear more child-like, since his character includes the trope "looking innocent despite being a supposed bad guy." Children are usually curious about their surroundings, so this animation may be done to imitate that, especially given how he didn't just glanced at it, his head actually fully turned to what he was looking at.

However, he also said this:

So he's not that curious, since he's already familiar with the surroundings. Not to mention how, the White House corridor and basement hallway is quite bare.

Another child-like quality could be the mere sense of wonder. Like, "Wow, so this is the White House" "Wow, they have this kind of elevator here?" "Wow, it looks just like my base." In which case, yeah, possible I guess. That could also tie in with his idealistic/optimistic world view, after remaining hopeful despite everything that he went through.

It might also be a character quirk, which further implies the kind of person he is. And that in itself opens up other possibilities:

Neurodivergence - I can't talk about this given how limited information we have. But the possibility is still up there.

Observant - I argue that an observant person doesn't need a full head turn. If animated, the character's head can make small turns or just, glance, like what Daryl does actually.

Detailed-oriented?... He's thoughful alright, but I can't say if he really sees the finer details, or if he's just careful when needed. Does potential germophobe count?

And lastly, he could simply marvel at any new thing after staying in his base/headquarters for so long, since he was always working in the background (or should I say, the Backyard?), and he always gave his physical errands to Raven. So, I'm guessing that this might be one of the few times that he went out, without hurrying too. It's not like he can see clearly with his hood in Overture and Xrd... Can he?

Welp, whatever it is, it's now a part of his charm 💕