Your semicolon is grammatically correct.
REVIEW
Plot
It's got a clear objective and stakes, and the pacing flows nicely. I assume you'll tell us why the mage needs killing pretty soon.
Right now it reads as a bit basic— but this is just a small snippet, so that's forgivable.
SPAG
"It stains your teeth, you feel the taste of iron on your tongue, but your laughs continue all the same"
Should have "and" before "you feel". Any joined independent clauses need some kind of conjunction, though there are artistic exceptions. I feel like this wasn't meant to be that. I'd also debate the necessity of a comma before the "and" once that adjustment is made, but it's still not wrong.
There's some awkward wording, too. For one, it should be "clattering steel", not "steel clattering". Adjectives tend to go before the noun they modify. It's also perfectly viable and even suggested to do without phrases like "the sound of" (found in that same sentence) to make things seem more immediate and avoid a narrative disconnect. If you want to get really deep into it, consider the fact that the word you present first will have more of an impact on the reader's mind. When you say "clattering steel," you’re immediately focusing on the active, noisy quality of the steel. It emphasizes the sound first, painting a vivid picture of metal in motion. "Steel clattering" splits the impact, focusing on the object first, then the action.
"Cannonball" is one word
You're also missing a couple apostrophes. "Man's mouth" vs "mans mouth", and "don't" vs "dont".
You push off his body, causing his bones to break under you, as if his body were being crushed under a stone.
That second comma is unnecessary. You do need the first comma; it separates the main clause (you push off his body) from the participial phrase (causing his bones to break under you). Standard grammar. The second comma implies that the final (dependent) clause is some kind of interrupting aside rather than the direct continuation that it is. It breaks up the sentence's natural rhythm, leaving it a little disjointed.
You take the second to take stock of the remaining enemies. Two guards on opposite sides of the room, the target, and a mage directly beside him.
The sentence fragment there works, though I think it would be smoother with a colon after "enemies" instead of a period.
No need for the comma after "gaudy" in "big, gaudy, throne chair"
Extra "the" in "The word pierces the through the air like a javelin"
There are more but I lost interest in pointing them out, and this gives you a basic idea of what to look out for anyway.
Except this one: "Maybe you’ll let her live, killing a sparrow could draw unwanted attention, even if it is unlikely." That's a comma splice. You could put a semicolon instead of the first comma, or a period. The first keeps the sentences more connected, while the second allows for more of a dramatic pause.
World Building
The magic system's got potential, I'll say that much. This whole "authority" thing with verbal commands is pretty neat. And I like the little details like the bronze badge with the bird; that's the kind of specific stuff that makes a world feel real.
But, this could be literally any fantasy world ever. Throne room? Check. Corrupt noble? Check. Magic users with hierarchies? Check. It desperately needs the fleshing out that further writing would hopefully grant it.
Characters
Our protagonist has... personality? Sort of? They're snarky and violent, which is something. The internal monologue stuff works well enough; at least we know what they're thinking while they're murdering everyone.
But holy cliches, Batman! We've got:
- Edgy assassin who laughs while killing
- Mage who goes from "I AM AUTHORITY" to "pls don't kill me" in 0.2 seconds
- Evil noble who literally just exists to die
- Guards who are disposable NPCs with no personality
Even small characters need some kind of distinction.
Other Thoughts
Credit where it's due: the action's clear. When window-smashing-assassin-person does their thing, I can picture it. The mix of stabby-stabby and thinky-thinky keeps it from being just mindless action.
It might be trying a little too hard to be edgy, though. The excessive gore is giving "mortal kombat" in the way that it seems a little more gratuitous than actually beneficial to the narrative. Written by teenage boys, for teenage boys (and like-minded creatures).
I like the bolding of the spells.
Final Overview
Is it terrible? Nah. It's actually pretty solid. There's potential here— the action flows well, and some of the ideas are interesting.
Oh, and it's a shit ton better than Tig's word vomit, so kudos.