In some circumstances, I have heard of employers asking prospective employees to expose their social media accounts during the hiring process.
In most cases, this seems to be just a formality check of “Is this person exposing their previous company’s info / making threatening statements / generally being an asshole of some kind?” or, in one case, to determine if someone was an anti-vax/anti-science type before they started a medical position.
This wasn’t done by an “agency”, though, and they really didn’t look that deeply. In some cases it seems to come with a wink-wink, nudge-nudge “So these are tooootally all your accounts, riiiight?”
Small horses, like small dogs, are herd animals, are utterly convinced they are ten times their actual size, and will show this off at any opportunity.