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/reservedTurnStore.ts

@@ -1,5 +1,5 @@
 import {
-    createPostgresConnector,
+    createGamePostgresConnector,
     type InputJsonValue,
     type TurnEngineDatabaseClient,
 } from '@sammo-ts/infra';
@@ -269,10 +269,10 @@ export class InMemoryReservedTurnStore {
 export const createReservedTurnStore = async (
     options: ReservedTurnStoreOptions
 ): Promise<ReservedTurnStoreHandle> => {
-    const connector = createPostgresConnector({ url: options.databaseUrl });
+    const connector = createGamePostgresConnector({ url: options.databaseUrl });
     await connector.connect();
     const store = new InMemoryReservedTurnStore(
-        connector.prisma as ReservedTurnDatabaseClient,
+        connector.prisma as unknown as ReservedTurnDatabaseClient,
         {
             maxGeneralTurns: options.maxGeneralTurns ?? DEFAULT_GENERAL_TURNS,
             maxNationTurns: options.maxNationTurns ?? DEFAULT_NATION_TURNS,