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/prisma.config.ts

@@ -2,20 +2,33 @@ import 'dotenv/config';
 
 import { defineConfig } from 'prisma/config';
 
+const resolveSchemaName = (value: string | undefined): string => {
+    if (!value) {
+        return 'public';
+    }
+    const trimmed = value.trim();
+    return trimmed ? trimmed : 'public';
+};
+
 const buildDatabaseUrlFromEnv = (): string => {
     const host = process.env.POSTGRES_HOST ?? '127.0.0.1';
     const port = process.env.POSTGRES_PORT ?? '15432';
     const user = process.env.POSTGRES_USER ?? 'sammo';
     const password = process.env.POSTGRES_PASSWORD ?? '';
     const dbName = process.env.POSTGRES_DB ?? 'sammo';
-    return `postgresql://${user}:${password}@${host}:${port}/${dbName}?schema=public`;
+    const schema = resolveSchemaName(
+        process.env.POSTGRES_SCHEMA ?? process.env.DATABASE_SCHEMA
+    );
+    return `postgresql://${user}:${password}@${host}:${port}/${dbName}?schema=${schema}`;
 };
 
 const databaseUrl =
     process.env.DATABASE_URL ?? buildDatabaseUrlFromEnv();
 
+const schemaPath = process.env.PRISMA_SCHEMA ?? 'prisma/game.prisma';
+
 export default defineConfig({
-    schema: 'prisma/schema.prisma',
+    schema: schemaPath,
     datasource: {
         url: databaseUrl,
     },