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/logRepository.ts

@@ -1,5 +1,4 @@
-import { LogCategory, LogScope } from '@prisma/client';
-import type { Prisma, PrismaClient } from '@prisma/client';
+import { LogCategory, LogScope, type GamePrisma, type GamePrismaClient } from './gamePrisma.js';
 
 export interface LogQueryOptions {
     limit?: number;
@@ -21,9 +20,9 @@ export interface LogEntryView {
 }
 
 const buildPaginationWhere = (
-    base: Prisma.LogEntryWhereInput,
+    base: GamePrisma.LogEntryWhereInput,
     options: LogQueryOptions
-): Prisma.LogEntryWhereInput => {
+): GamePrisma.LogEntryWhereInput => {
     if (options.beforeId) {
         return {
             ...base,
@@ -34,16 +33,16 @@ const buildPaginationWhere = (
 };
 
 const buildFindArgs = (
-    where: Prisma.LogEntryWhereInput,
+    where: GamePrisma.LogEntryWhereInput,
     options: LogQueryOptions
-): Prisma.LogEntryFindManyArgs => ({
+): GamePrisma.LogEntryFindManyArgs => ({
     where: buildPaginationWhere(where, options),
     orderBy: { id: 'desc' },
     take: options.limit ?? 50,
 });
 
 export class LogRepository {
-    constructor(private readonly prisma: PrismaClient) {}
+    constructor(private readonly prisma: GamePrismaClient) {}
 
     // 전역(시스템) 로그 조회
     async listSystemLogs(