Extend friend grouping to the lobby team preview

The preview was calling assignTeams without friend data, so the
team layout shown in the lobby could differ from the layout the
game actually started with. Wire friends through ClientInfo so
the preview matches.

Extract the publicId→clientID translation used by both start()
and gameInfo() into buildFriendsLookup() to remove the duplicate.

src/core/Schemas.ts

@@ -156,6 +156,7 @@ const ClientInfoSchema = z.object({
   clientID: z.string(),
   username: UsernameSchema,
   clanTag: ClanTagSchema,
+  friends: z.array(z.string()).optional(),
 });
 
 export const GameInfoSchema = z.object({
@@ -192,6 +193,7 @@ export interface ClientInfo {
   clientID: ClientID;
   username: string;
   clanTag: string | null;
+  friends?: ClientID[];
 }
 export enum LogSeverity {
   Debug = "DEBUG",