A medieval empire the size of South America would be vast.
The area of South America is about 17,840,000 km2 (6,890,000 sq mi). According to Wikipedia, the only empires in history larger than that would be the British Empire, the Mongol Empire, and the Russian Empire.
It would probably also contain large bodies of water which would have different rates to sail across than to travel the same distance on land.
And your ideas about the organization of such a vast medieval empire seem rather simplistic.
Legally, the vast majority of the human population are considered subjects of whatever noble rules where they were born and can only leave said noble’s lands with permission.
Legally, the entire population of the Empire will be subjects of the emperor. And if the empire has feudal lordships, the natives of a fuedal lordship will be subjects of their feudal lord, as well as subjects of the emperor.
But remember, in feudal Europe, most feudal lords of manors were vassals of the local count, and most counts were the vassals of their local dukes and all Dukes were vassals of the king - if they weren't vassals of the king, they were outside his kingdom.
So in a feudal empire, you might suppose that the average peasant was the subject of:
his local lord.
- The Emperor.
But that is an oversimplified hierarchy considering the vast size of the empire in your story.
According to the Wikipedia list, the Mughal empire around 1700 had only about 4,000,000 square kiometers of land area, only about 0.224 of the aea of South America.
And most of the empire consisted of provinces administered by appointed governors. So you wouldn't think there was much room for vassal kings, and vassals higher than kings. But there were a number of vassal state within the Mughal Empire, just as there were within the British Raj of India.
The Mughal Padishahs grant a number of titles to their Hindu subjects and vassals, including many which were more or less noble ranks. The lowest royal title granted by the Mughals was raja, king, and the ranks of royalty went up from there.
Raja - king.
Raja Bahadur - illustrious king.
Maharaja - great king.
Maharaja Bahadur - illustrious great king.
Sawal Maharaja Bahadur - elevated illustrious great king.
Rajadhiraja - king of kings.
Rajadhiraja Bahadur - illustrious king of kings.
Maharajadhiraja - great king of kings or king of great kings.
Maharajadhiraja Bahadur - illustrious great king of kings or illustrious king of great kings.
My answer at
also includes examples of Kings of KIngs who were vassals of Roman Emperors. It also mentions that the High King of Medieval Ireland could be considered to be a king of kings of kings of kings.
Your empire is so vast that the various vassal kings should not be subject only to kings of kings. The kings of kings need to be subject to Kings of kings of kings and so on up to the Emperor.
And presumably the Emepror would also be the lord of many lordships, the count of many counties, the duke of many duchies, the king of many kingdoms, and king of kings and king of kings of kings, and so on, in order to have enough areas under his direct rule to maintain his authority over the other kings, kings of kings, kings of kings of kings, etc. in the empire.
Or perhaps the imperial domain at the center of the empire would consist of a region the size of the Roman Empire, for example, directly administered by appointed officials at various levels, with tax collection to support a well trained and well equpped army of hundreds of thosuands of men, more powerfull that all the feudal levies of the vassal kings, kings of kings, kings of kings of kings, etc. combined.
So an ordinary peasant in your empire might be the subject of many different levels of lords and kings up to the Emperor. And with that many levels of persons the peasant is a subject of, one of them would die and be succeeded about every other year. So you need to restrict the number of levels of lords that a person would be obligated to return home every time a new lord inherited. Otherwise your traveler would have to return to the headquarters place of some lord above him about every other year.
And medieval European peasants had several different legal and social classes.
Some peasants were slaves, the personal property of the lord of their manor, and could be bought and sold. Some peasants were serfs, who were legally tied to the manor, and whose relationship with their lard was a matter of the feudal customs, sometimes open to negotiation. Other peasants were free persons who rented lands owned by the lord of the manor and had more freedom to negotiate terms with him.
And it was perfectly possible for peasants to be free persons owning their land, which would not be part of any manor, and so they were only subordinate to whoever had political and legal jurisdiction in their region. Many peasants did own their land.
And medieval empires varied in how urbanized they were, but most had a number of towns and cities with populations who were not subject to any feudal lord.
So what social class of person would be most likely to become a travelling merchant?
A free resident of a town would be the most likely, And a younger son of a free land-owning peasant who wouldn't inherit his father's farm would be the next most likely, and so on down to least likely, a slave. Any sort of serf with many legal obligations to his lord would be the second least likely class of person to become a merchant.
So you need to create a special (and very small if your society is like Medieval Europe) class of persons for your story, who are sort of slaves or serfs of a feudal lord, and have many obligations to that lord, but for some reason have permission to travel extensively, with an obligation to return periodically to account for their doings on their travels, and to return when the lord dies and swear allegiance to his heir, the new lord, and renew their permission to travel.
And they should face legal penalities for failure to return within a specified time. Those might be civil penalties or criminal penalities for their relatives remaining at the manor. And your particular character may have family members at home who would face exceptionally harsh and severe punishment if your character failed to return in time, due to some very special circumstances such as a crime, punishable by death by torture, which a relative has been convicted of, with the punishment deferred as long as the traveller fulfills all his obligations including returning in time when required.
Perhaps the character's role of a merchant is just a cover for some secret mission(s) he carries out for his lord, though he is free to make a profit from it if he can.