I'm going to deviate from a lot of Batman fans on this, but I don't think the Court of Owls is the most enticing story for this Batman,
so far.
- The Batman was already about uncovering that the systems in place (police, courts, etc.) are all corrupt and working in tandem. Having The Batman: Part II or even Part III cover the Court of Owls would feel way too much like a repeat. "You think Gotham was corrupt in the first film? Well, just wait - Gotham's gonna corruption even harder in the sequel!" There's not really any element of surprise for the audience at that point, and the characters have already been confronted with the fact that Gotham is rotten to the core.
- The Court of Owls works best as a story for a more seasoned, many years into his career Batman. Why? Having a seasoned, kick-ass Batman who's been at the top of his game for quite awhile suddenly learn that he's not noticed a secret society of corrupt, evil Gothamites operating under his nose is a huge deal and a blow to his worth as a detective and a guardian of Gotham. Having it occur to a new Batman just doesn't hit the same - it'd be like remaking Logan (2017) with a younger Wolverine.
Having the Court of Owls occur to a 2-year Batman undercuts the significant emotional/mental ramifications for Bruce that is an essential aspect of the story's depth, by a huge margin.
I think there are far more themes worth exploring, honestly. If Reeves wants to do Court of Owls in a story set much later in this Batman's story, when he's been around awhile, thinks he has seen it all, etc., I'd be all for it.
But a Year 2 Batman? It just doesn't hit quite the same and using it so early takes away a huge reason why the story rocks, from a character perspective.