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/turn/turnDaemon.ts

@@ -30,6 +30,7 @@ export interface TurnDaemonRuntimeOptions {
     profile: string;
     profileName?: string;
     databaseUrl: string;
+    gatewayDatabaseUrl?: string;
     defaultBudget?: TurnRunBudget;
     clock?: Clock;
     controlQueue?: TurnDaemonControlQueue;
@@ -137,6 +138,7 @@ export const createTurnDaemonRuntime = async (
         options.profileName
             ? await createGatewayProfileGate({
                   databaseUrl: options.databaseUrl,
+                  gatewayDatabaseUrl: options.gatewayDatabaseUrl,
                   profileName: options.profileName,
                   cacheMs: options.pauseGateIntervalMs,
               })