If a Clockwork Soul Sorcerer is in a social situation and has disadvantage on a persuasion check, then uses their Restore Balance feature, would anyone be able to see that?
It's up to the DM. I would rule it is imperceptible.
The Restore Balance feature does not have much helpful flavor text to tell us what the sorcerer is doing:
Your connection to the plane of absolute order allows you to equalize chaotic moments.
There's nothing here or in the rest of the feature description that tells us the sorcerer is doing anything outside of their own mind when they use this feature. This is why I would rule it is imperceptible, but it is also why there is plenty of room for a DM to make a different ruling.