I don't think it was a power up, I think it was more of a show of a power.
I have some things to note, after going through all we have, Kai has gates (of power) in chapter 3.
And as the Beast Goddess said, each is exponential and he has a cap of three and he could die if he reaches there.
Going back to Chapter 1, his berserk mode was his full power, I don't think people noticed the detail but he had three circles on his neck/back behind him.
He has a ton of power he just isn't very experienced in using it, that's why he undergoes practice in all routes.
I agree with you as this was a show of power AND a power-up.
The Queen fight is the first time he has awoken his celestial powers (in beastial form), and that wasn't a show of power, that was needed, the Queen couldn't give two fucks about someone who claimed he could beat her and then get thrashed.
The Queen didn't get scratched even and the game has a ton of attention to blunt hits and blood, I personally think she is at gate one level.
The scenes afterward weren't insults to the King.
Think about it, put yourself in the shoes of the captains.
A guy shows up claiming he beat the Queen and the Queen adores him out of the blue?!
You're going to be at least skeptical and want proof, not to mention the beasts... usually act a little beastial.
I don't think Kai has ever used two gates up until this point (other than his berserk mode) with the dragon captain.
There's another symbol behind the main circle during the fight with the dragon captain and it is implied by the Queen that this power wasn't his normal stuff.
(Because he only achieved gate one when fighting with her)
From a storytelling point of view, I think the game (although flawed in some aspects) is well-written.
It is up to the player to decipher what happened, and the implications and meanings of actions taken in this game.
It believes in the player/audience that they will connect the dots between all three routes and see the wider picture.
Typing this just makes me want to play more God's Call lol