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.

packages/infra/src/gamePrisma.ts

@@ -0,0 +1,18 @@
+import { PrismaClient as GamePrismaClient } from '../prisma/generated/game/index.js';
+export {
+    LogCategory,
+    LogScope,
+    Prisma as GamePrisma,
+} from '../prisma/generated/game/index.js';
+export type { PrismaClient as GamePrismaClient } from '../prisma/generated/game/index.js';
+
+import type { PostgresConfig, PostgresConnector } from './postgres.js';
+import { createPostgresConnector } from './postgres.js';
+
+export const createGamePostgresConnector = (
+    config: PostgresConfig
+): PostgresConnector<GamePrismaClient> =>
+    createPostgresConnector(
+        config,
+        (options) => new GamePrismaClient(options)
+    );