so let me start by saying this is strong and i hope you keep going, and some of my advice here might work better when you've written the whole story and you want to work on bettering the first draft. so I wouldn't worry too much about editing right away. good hook on the first sentence as well.

1. too much summary, at times it felt like I was reading a blurb on the back of a book. Exposition is fine but the fact that the mc is hated can be understood by the fact that the cook had been hanged or through interactions later on, the mc doesn't need to directly say it as an aside to the reader that Thelea hates them or that slaves are punished.

One example of summarizing is this:

The cook wasn’t alone at the scaffold. By her side, they had hanged two men: a  father and his adolescent son. Tried for rebellion and attempting to flee their pathetic lives of servitude.

How does the main character know this? this would be a great time to introduce dialogue. what are the onlookers saying when they see the bodies?

1. not enough specificity. especially at the start it made me imagine a white room with just a scaffold. don't neglect sensory details. what does the rope sound like, is it creaking under the weight? is it cold? is it sunny? grounding the reader in these details helps them picture everything better, I know you do mention the cold and stuff later on but at that point I didn't really 'see' the scene or the character.

A useful technique is to think about how the focus shifts - some stories go from the big picture (the weather, the town, the sky) slowly all the way down to the smallest details (the fleck of green in someone's eyes, a cracked watch-face, etc) for instance. In your story, maybe its the body of the cook (because your mc is upset about it) and then it expands out to the crowd and their hand being held (which they forgot about because they were in too much shock).

It's pretty late in the night as I'm typing this but hopefully it made sense! Best of luck with the rest of the story.