Scope live chat to the current match and save match history

src/lib/game-chat.ts

@@ -17,9 +17,10 @@ export interface ChatContext {
     round: number | null;
 }
 
-export type ContextualChatEntry = ChatEntry & { context: ChatContext };
+export type ContextualChatEntry = ChatEntry & { context: ChatContext; matchId?: number };
 
 export interface ChatMatch {
+    id?: number;
     startedAt: string;
     endedAt: string | null;
     lastReceivedAt: string;
@@ -174,6 +175,6 @@ export function enrichGameChatTimeline(lines: readonly string[], options: {
             }
         }
         if (entry.type === 'boundary' && entry.event === 'end') logEnded = true;
-        return { ...entry, context };
+        return { ...entry, context, ...(match?.id === undefined ? {} : { matchId: match.id }) };
     });
 }