Which is weird tbh. MC goal is to prevent the war. So unless he killed Finn himself, the first thing he should do is to go to templars to get their side of the story and, if possible, try to deescalate. He still have access to templar's base so he doesn't need Kaija nor his parents for this. Instead he goes "oh well, i guess there is a war now" and does nothing.
At this point I wonder how all different paths will be connected without ignoring player's choices
No he can't. There's a big difference between being able to enter the base and having access to a council chamber where his father the grandmaster currently is and trying to gain access to a prisoner in the dungeons. It's not like he can pop in there while pretending to look for the bathroom.
As for stopping the war, how? He's one man and he barely knows his way around one city in Neverwhere. He has no power, no way of communicating, no money, nothing.
At this point the war is inevitable, and the only way to stop it once it gets going is to prove a third party instigated both sides. For that he's going to have to explore a lot more, get a lot stronger, and gather some powerful allies.
Now, he's very, very lucky in a way, because if he does actually find proof, he is someone both sides would listen to, at least assuming he didn't kill Finn himself. He knows the leaders of both groups.