feat: add database schema support for gateway and game profiles

- Introduced `dbSchema` configuration option in GatewayApiConfig and GatewayOrchestratorConfig.
- Implemented schema resolution logic in environment configuration functions.
- Updated context and orchestrator factory to use GatewayPrismaClient instead of PrismaClient.
- Refactored orchestrator server and profile repository to accommodate new database schema handling.
- Created separate Prisma schemas for game and gateway in the infra package.
- Enhanced Postgres connector to support schema overrides in database URLs.
- Updated documentation to reflect changes in database schema handling.
- Added new Prisma generation and database push scripts for game and gateway schemas.

app/game-engine/src/turn/worldLoader.ts

@@ -1,5 +1,5 @@
 import {
-    createPostgresConnector,
+    createGamePostgresConnector,
     type JsonValue,
     type TurnEngineCityRow,
     type TurnEngineDatabaseClient,
@@ -252,10 +252,10 @@ const mapTroopRow = (row: TurnEngineTroopRow): Troop => ({
 export const loadTurnWorldFromDatabase = async (
     options: TurnWorldLoaderOptions
 ): Promise<TurnWorldLoadResult> => {
-    const connector = createPostgresConnector({ url: options.databaseUrl });
+    const connector = createGamePostgresConnector({ url: options.databaseUrl });
     await connector.connect();
     try {
-        const prisma = connector.prisma as TurnEngineDatabaseClient;
+        const prisma = connector.prisma as unknown as TurnEngineDatabaseClient;
         const worldState = await prisma.worldState.findFirst();
         if (!worldState) {
             throw new Error('world_state row is required to start turn daemon.');