Thank you for sharing your first chapter. Your world-building is on the level of Sara J. Maas in my opinion! I loved how you crafted the cold, inhospitable landscape and the grimness of the inn. The 'shroom' -everything is a great touch too. The language you use is sophisticated and a joy to read. I also think you have differentiated between your characters well with the way they think and the language/tone they use in dialogue.
Only a couple of things: 'stared back impassively' appears on two occasions quite close together. The other is that when the High Tas halted in front of Kayne to exile him, I thought he was in front of Ancel because of the previous sentence. The 'him' identifier confused me. I don't know if that would happen to everybody. It might just be me!
My only other comment is really very subjective, and you can take it with a pinch of salt! It is a stylistic point. There are a few places where I felt a comma was too weak to use as the junction between clauses. I can see you aren't a semicolon hater since you've used it on five occasions. Sometimes a full stop can be effective as well though. I don't know if anybody will agree with me. Here are some examples where I felt there were two main clauses in the sentence:
Ander stood, he’d be damned if he’d let the man loom over him.
He had his eye on the office of High Tas, and if he ever succeeded, Goddess help the Fluxers in his care, he made no secret he thought they should all be killed.
All that was left of the old smithy was ruined walls and a chimney, the rest was underwater,[...]
The day wore on and worry grew, he couldn't wait much longer.
Strapping on his weapons, the long sword on his back, its pommel rising above his left shoulder and his short blade at his right hip, he found their familiar weight reassuring.
As I said, ignore me if this is your style! I am not an expert by any means.
Anyway, this opening captured my interest and I look forward to reading more with great anticipation.