If it's fictional, you can literally make up anything, because the stories you're referencing sure do. The characters aesthetically look a bit like the nobility of around the 17th-18th Century Europe in terms of fashion and architecture, but the rest is largely just made up based on whatever the creators think would be cool and Romantic (capital R Romantic, as in Romanticism, not like... small r romantic as in relating to love). Like the men all have these fashionable modern short hairstyles; nobody's wearing a powdered wig, and they wear long dress pants from the 19th or 20th century instead of breaches and stockings. Oh and their maids and butlers all dress like they're in Victorian Britain while serving people who dress like they're in pre-revolutionary France, and they all eat foods that look distinctly modern. If you've been doing research and it's coming up short, it's probably because you won't find anything that clearly lines up with how things work in these novels, because they're a fantasised ideal of roughly 17th-18th century European nobility as imagined by a modern young person in an East Asian country who is more interested in the aesthetic than the (often less attractive) historical reality.
All you really need to is make your world feel like it's running on some kind of logical sense.
So, the scenario: You are a noble and the monarch has called you to the capital for some reason that, presumably due to distance, will require a fairly long trip and a stay of multiple days or longer before you go home.
Cars aren't invented, but you don't want to look like a peasant or get dirty so you're probably in a carriage. Carriage needs horses and a driver, so you'll need one or more coachmen and probably a groom who can look after the horses.
A carriage is a juicy target for highwaymen, so you'll need a few guards. Not TOO many though, you don't want to look like you're leading an army to the King/Queen's gates! So maybe just a handful of guards decked out in nice livery so they look cool.
If you're a lady or if you're bringing your wife or daughter along, you'll need one or more "ladies in waiting" or "ladies maids" because it's legit impossible to put on the noble clothing of that era on your own if you're a woman. It's also a sign of your status.
If you brought kids along, they'll need some kind of nurse, caretaker, governess or tutor. You're a noble! You don't look after your own kids!
You'll probably want some sort of advisor/visier/clerk/squire/butler to be basically your PA.
If you're often ill, you may take a physician along (this might be a wizard or something in Fantasy settings).
If you're religious, and especially want to show how religious and pious you are, you might bring a priest. (this priest may also double as advisor/clerk or as your kids' caretaker).
You will definitely want to bring some extravagant gift for the person you're visiting, since they'll be hosting your visit. If it's an animal (no, really... that was a thing in history, people gifting tigers and stuff), you might need a person to look after it.
If you want to show off, you might bring a bunch of hangers-on like other minor nobles who want to ingratiate themselves at court. This is also handy as a favour to nobles from your region. Take a friend's teenage daughter to introduce herself at court and they'll owe you a favour, plus if court like her, it'll reflect well on you! Even better if she bags herself a good husband.
This is a fairly general list applicable across many european and asian cultures because the stuff people needs tend to stay fairly consistent. The bigger your retinue, the more important you'll look. In fact it was a well-documented "power move" to turn up with a massive retinue that put a strain on the host. Most minor nobles would just have a few people though because you have to pay them and still have staff to guard and manage your household.
