Kill him

welcome to life before the modern era lol. everyone is nothing but classist

Wait, he's a servant tho, no?
I understand that still miles away from being a noble. Still being a slave is horrid thing on different level, like you hardly can expect anyone to treat you like a human

He's not a slave???... He's just a servent

Cause of your reply I realized that original poster titled it 'kill him' wooooah
And yeah, I said the same thing as you

Y'all need to use a little context clues people not everything needs to be spelled out he can't quit on his own nor does he get paid what would you call him?

Let's ask ppl that had slaves on their ancestors or are slave today if being a servant even in these conditions is the same as slave, shall we?
He absolutely can quit
Other ways to earn money for him could be: woodcutter, often would be man even alone going into forrest, cut wood, seel in market, could also collect some herbs, mushrooms, berries on the way and sell em too. Let's say he can't go get hired in another place, meaning servant in another house, which would be obvious option. He can do odd jobs as like construction, some carrying stuff, fixing, chopping wood, etc for other common or noble folk. He can become farmer and do fishing. Most likely he's paid, actually, I don't know why you think he isnt. The only possibility he isn't is if he messes up and damages, ruins stuff a lot, so they take it from his salary.In the very least he's given place to live and nice food. At first he had to go into this house cause he didn't anywhere else to go, just isekaied and so on. Now that he's familiar with his surroundings a bit more: big healthy guys like him had many ways to earn money. Especially if he makes a plan of leaving in warm part of year, he could even just stay for a while in nicely arranged cave or like temporary hit, while saving to get a house or slowly building a house or restoring some abandoned ones, villagers often would help each other. Unfortunately, he probably wouldn't be able to use his writing/reading skills from the future cause at that time in Joseon they were writing with Chinese symbols, but who knows.
If you're implying that his master wouldn't let him go and would like create obstacles for him to work otherwise, there're ways to run away to another village and use different name. He even could join like bandits in the forest, or actually become a butcher or do graveyard work, ppl of that class were considered separate from everyone else, lived separately and often had their own militia, so hide amongst them was easy. Yes, labour was rather awful, so not that many wanted to do it. But most of the ppl didn't have it easy.
Now SLAVE wouldn't be able to do any of that
Their relationships are of course not equal, but calling smn slavery when it's not, is minimazing the horrors of being actual slave, when it's not just one or few ppl dont see you as human, when the whole state, everyone is in the right to treat you as commodity and whichever way they please

I'm black american I don't need to research to know about historical slavery but you definitely need to because there are different kinds across the globe please research korean servants and slavery where the author and this story come from specifically. regardless of you thinking he could pick up a second job somewhere he still wouldn't be getting paid from his main job ergo he's a slave. I dont know why you think someone running away means they're not a slave please look up the underground railroad so you can dispel that notion immediately. also literally the chapter before this people were treating him as a commodity and saying he didn't know his place this happening in public shows how society and the state treats him. he literally relates his situation with the little boy who was called a slave and sold for a bag of rice I don't think you know the context because you need it spelled out but hes a slave

He's a slave

No he's not

He is

Who was talking about second job? Yes, surely, noble house wouldn't like their servant having another job, same as some business would do now
Running away can be for different reasons
In the example I gave it was more akin smn even in our day and time running away from abusive partner, especially if that smn has money and influence, still it is different from slavery
I have researched lives of servants and slaves in Joseon, yes, and therefore my examples of what servants could do and slaves couldn't
Yes, lower class ppl could be mistreated and be treated poorly, even now smn can be entrapped not depending on their class and be treated even as a slave by one person or group of ppl. That doesn't make this person a slave. Being a slave means not having human rights, it has to do with legislation and its execution in particular state, in particular periods of time. So, with the example of person trapped, that would be human trafficking, and would make this person captive, kidnapped, wouldn't make that person a sin actual slave, as by law he's not, meaning that at least theoretically those who captured him should be punished and he could seek justice. Actual slaves don't have rights to do that in any scenario possible, that is never an option to them.
With respects to your heritage, I won't speak of black slavery, but I can speak about cases of present slavery around the world, like in Middle East, totalitarian regimes that put ppl in very similar position and historical European slavery cases, which yes, existed. Korean enslaved Korean ppl, many eastern European were enslaved by western European, tatar Mongols. I would even say that some cults had cases close to slavery, however still, not, as most of them still were within bounds of current or recent American and European laws, so technically speaking they had ways to seek help and escape.
By law of the country he is in and time period he can leave, he's hired and not owned, he can't be sold or purchased. If we talking about specific cases when smn unlawful is done, which yes, I do not deny would happen and more often to say 'rare', that would be against the law and justice could be sought after. But if we include separate individual cases that would operate outside of law to change definition of things. Then anyone is a slave under an emperor. It was not rare for nobles to be accused of treason, and become government slaves, tho they were innocent. Were all women and children enslaved too? Were prostitutes and kisaengs slaves? Readers and other in-hire artists? They were treated often same, weren't paid and had no freedom of choice
Basically all of that can be described in 'living like a slave'. However, I have bigger respect to all those that were and are absolutely stripped of all dignity and agency and have to exist in the despair that most of us never even get a taste of, to equate all that to experience of an actual slave