Out of curiosity, if Augus had been in a more stable frame of mind, would he still have compelled Jack to discharge his power in Ch 23? Augus knows how much Jack's power has increased having seen it first hand. Gwyn was taking a calculated risk in assuming Augus would have Jack discharge it like he normally does, but if Augus was more stable, would he have still done that? Because I feel as though that would have changed things a lot. Yay hypothetical questions :)
If Augus had been in a more stable frame of mind in chapter 23, he would have a) reassembled a new Inner Court by then and gotten *them* to scope out the situation, b) known that Jack's revenge plot was a trap, c) not turned up.
To be honest if Augus was in a stable frame of mind that encounter would never, ever have happened at all. Gwyn was really betting on Augus' unstable sense of self. He knew that if Augus turned up - he'd automatically ask Jack to discharge his power, that is something Augus does as a habit even when he's stable, with enemies. Gwyn also knew that if Augus didn't turn up - it would be a sign that Augus was more stable than he'd thought, Jack would be safe-ish, and it would be time to reassess.
Gwyn knew he was taking a calculated risk, and as soon as Pitch was like 'I can read Augus' fears and hey they're all about the fucking Nightmare King what's with that,' (at the dome confrontation) Gwyn was like 'no this is GOING TO WORK.' Like, he knew without a doubt, after that conversation with Pitch. If there's one thing Gwyn can do, it's exploit the weaknesses of others. He's so used to hiding his own, he's good at spotting them in others and using them. He is the master of 'getting things done,' and he will do that by whatever means he has to. Whether that's exploiting Ash's love for his brother, Jack's need to get rid of Augus to sleep better at night, Pitch's love of Jack, or Augus' terror of the Nightmare King. So... yeah.
Anyway, if Augus had been stable then actually, welp, probably he would never have become King in the first place. He wasn't interested in status like that when he was mentally stable. He wasn't ever interested in being King. He didn't ever want to leave his lake. 'If Augus was stable,' would have changed everything.