Slavery and Smartphones in the same era? Seems weird, but sure
Do you really think that just because humanity is more modern nowadays that slavery doesn't exist? Shit, there's even concentration camps in China and who knows where else being kept in secret.
People say "never again" but it still happens.
In the US it's broken into two main categories: sex trafficking and labor trafficking.
Usually those forced into sex work are shuttled off to other countries where it's easier to control their victims and fly under the radar of law enforcement, but certainly not all. It's a very black market sort of affair.
Those forced into labor are either forced to work on farms or do other sorts of manual labor, or are forced to work in the homes of people who have the monetary and social means to keep their "servant", servile, with threats, manipulation, isolation, debt bondage, etc.
Kaede in this story appears to have been forced into both, given her reactions we've seen already; and despite her new mistress being pretty benevolent so far, it's still forced labor under the premise of Kaede being property and not a person. So... yeah. It's realistic. Weird? Yeah, also weird that this goes on in the real word. But yeah...