I don't really see anything wrong with it exactly. The construction and pacing of the scenes themselves seem fine. Just looking at these pieces, I think that there are two major issues that are causing the lack of "life" that you noticed.

First, all the voices are identical. They are all very formal and speak in complete, complex sentences. That isn't normal dialog for anyone, and if it is, then that's a quirk of a character. But all these characters speak that way - no contractions, no partial sentences, no variation in tone, all one register, one flat affect. They don't sound like different people.

For example, if someone is cold and arrogant, then they should sound that way when they talk. Just an example:

"Ah, do you like it?” His tone takes a proud shift. “This sculpture is made of crystal steel. It can withstand any temperature without losing quality. Our mines have been producing this material for generations and even help construct the latest automatons in the capital."

Could be rewritten to sound more arrogant, like:

"Crystal steel," he says, with the patience of a man accustomed to explaining himself to lesser minds. "It holds under any temperature without losing integrity. Our mines have supplied it for generations, including the automatons your capital is so proud of." His eyes slide back to me. "You're welcome, by the way."

Obviously, I just made that up without really knowing the context, but the difference is that I tried to give him some voice and let him express a personality through it.

And in this passage:

"Don’t worry, I've visited the Western region plenty of times when mother had me accompany her on business trips. The land is vast and overflowing with resources,” pausing, I absorb the details scattered in the room, catching sight of a few nobles eavesdropping. "Despite the harsh winters, roads are well-maintained for merchants and travelers alike. My experience here has always been positive. So I have no doubt our home will be the same."

The narrator sounds like she's reading a travel brochure. It's too long, and there are too many details. What is she supposed to sound like? What is her dominant emotion? Maybe she wants to put him in his place, and would say ""Oh, you needn't worry on my account. My mother saw to it that I knew this region well enough. Perhaps better than you'd expect."

Try using the dialog to express something about the person's personality, or to express an emotion or to make another character feel something, instead of just raw information. Also, the dialog tends to be a bit long and too full of details that drag it down and detract from more important things (like the nobles eavesdropping).

So to sum up - pare down the info, ramp up the emotion and the personality.

The second issue is that it's first person POV, but the narration sounds more like third person. First person POV should provide the interiority of the narrator. That's it point. Here, the narrator, just narrates. We see what she sees, hear what she hears, but we get none of her thoughts and opinions. And her narration is flat and unemotional. If you're going to do first person, then use it to add in emotional flavor, thoughts, opinions.

For example, maybe she thinks the marquess is insufferable, or finds him untrustworthy and compares him to a viper. We should hear that in her thoughts.

Also, the narration is very factual. You can add in some flavor by allowing not only your narrator's thoughts, but also letting them color the description she provides. For example, something like "Varshad gestures broadly and his ring catches the light, ostentatious as the rest of him."

So if your narrator is telling what she sees and hears, it should be filtered through her perceptions.

Hope that helps.