feat(mcp): add MCP Server Integration — Property Search, Analytics, Valuation

Implement 3 MCP servers in libs/mcp-servers/ using @modelcontextprotocol/sdk:

- Property Search: NL search via Typesense, property comparison, detail lookup
- Market Analytics: market reports, price trends, district comparison
- Valuation: AVM integration with Python AI service, feature extraction, batch valuation

Includes NestJS integration module with SSE transport for in-process hosting.

Co-Authored-By: Paperclip <noreply@paperclip.ing>

apps/api/src/modules/mcp/index.ts

@@ -0,0 +1 @@
+export { McpIntegrationModule } from './mcp.module';

apps/api/src/modules/mcp/mcp.module.ts

@@ -0,0 +1,35 @@
+import { Module, type OnModuleInit } from '@nestjs/common';
+import { McpModule as McpCoreModule, McpRegistryService } from '@goodgo/mcp-servers';
+import { SearchModule } from '@modules/search';
+import { TypesenseClientService } from '@modules/search/infrastructure/services/typesense-client.service';
+import { LoggerService } from '@modules/shared/infrastructure/logger.service';
+
+@Module({
+  imports: [
+    SearchModule,
+    McpCoreModule.forRoot({
+      aiServiceBaseUrl: process.env['AI_SERVICE_URL'] || 'http://localhost:8000',
+      typesenseCollectionName: 'listings',
+    }),
+  ],
+})
+export class McpIntegrationModule implements OnModuleInit {
+  constructor(
+    private readonly typesenseClient: TypesenseClientService,
+    private readonly mcpRegistry: McpRegistryService,
+    private readonly logger: LoggerService,
+  ) {}
+
+  async onModuleInit(): Promise<void> {
+    this.mcpRegistry.setTypesenseClient(this.typesenseClient.getClient());
+
+    // Re-initialize servers now that Typesense client is available
+    await this.mcpRegistry.onModuleInit();
+
+    const servers = this.mcpRegistry.getServerNames();
+    this.logger.log(
+      `MCP servers initialized: ${servers.join(', ')}`,
+      'McpIntegrationModule',
+    );
+  }
+}

apps/api/src/modules/search/search.module.ts

@@ -40,7 +40,7 @@ const QueryHandlers = [SearchPropertiesHandler, GeoSearchHandler];
     ...CommandHandlers,
     ...QueryHandlers,
   ],
-  exports: [ListingIndexerService, SEARCH_REPOSITORY],
+  exports: [ListingIndexerService, SEARCH_REPOSITORY, TypesenseClientService],
 })
 export class SearchModule implements OnModuleInit {
   constructor(