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/scenario/scenarioSeeder.ts

@@ -1,5 +1,5 @@
 import {
-    createPostgresConnector,
+    createGamePostgresConnector,
     type InputJsonValue,
     type TurnEngineDatabaseClient,
     type TurnEngineEventCreateManyInput,
@@ -117,7 +117,7 @@ export const seedScenarioToDatabase = async (
         },
     });
 
-    const connector = createPostgresConnector({ url: options.databaseUrl });
+    const connector = createGamePostgresConnector({ url: options.databaseUrl });
     const now = options.now ?? new Date();
     const tickSeconds = options.tickSeconds ?? DEFAULT_TICK_SECONDS;
     const generalGold = options.defaultGeneralGold ?? DEFAULT_GENERAL_GOLD;
@@ -125,7 +125,7 @@ export const seedScenarioToDatabase = async (
 
     await connector.connect();
     try {
-        const prisma = connector.prisma as TurnEngineDatabaseClient;
+        const prisma = connector.prisma as unknown as TurnEngineDatabaseClient;
 
         if (options.resetTables ?? true) {
             await prisma.event.deleteMany();