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-api/src/server.ts

@@ -2,7 +2,7 @@ import fastify, { type FastifyRequest } from 'fastify';
 import cors from '@fastify/cors';
 import { fastifyTRPCPlugin } from '@trpc/server/adapters/fastify';
 import {
-    createPostgresConnector,
+    createGamePostgresConnector,
     createRedisConnector,
     resolvePostgresConfigFromEnv,
     resolveRedisConfigFromEnv,
@@ -35,7 +35,9 @@ const extractBearerToken = (value: string | string[] | undefined): string | null
 
 export const createGameApiServer = async () => {
     const config = resolveGameApiConfigFromEnv();
-    const postgres = createPostgresConnector(resolvePostgresConfigFromEnv());
+    const postgres = createGamePostgresConnector(
+        resolvePostgresConfigFromEnv({ schema: config.profile })
+    );
     const redis = createRedisConnector(resolveRedisConfigFromEnv());
 
     await postgres.connect();