feat(#27): implement intent classification service

Implement intent classification for natural language queries in the brain module.

Features:
- Hybrid classification approach: rule-based (fast, <100ms) with optional LLM fallback
- 10 intent types: query_tasks, query_events, query_projects, create_task, create_event, update_task, update_event, briefing, search, unknown
- Entity extraction: dates, times, priorities, statuses, people
- Pattern-based matching with priority system (higher priority = checked first)
- Optional LLM classification for ambiguous queries
- POST /api/brain/classify endpoint

Implementation:
- IntentClassificationService with classify(), classifyWithRules(), classifyWithLlm(), extractEntities()
- Comprehensive regex patterns for common query types
- Entity extraction for dates, times, priorities, statuses, mentions
- Type-safe interfaces for IntentType, IntentClassification, ExtractedEntity, IntentPattern
- ClassifyIntentDto and IntentClassificationResultDto for API validation
- Integrated with existing LlmService (optional dependency)

Testing:
- 60 comprehensive tests covering all intent types
- Edge cases: empty queries, special characters, case sensitivity, multiple whitespace
- Entity extraction tests with position tracking
- LLM fallback tests with error handling
- 100% test coverage
- All tests passing (60/60)
- TDD approach: tests written first

Quality:
- No explicit any types
- Explicit return types on all functions
- No TypeScript errors
- Build successful
- Follows existing code patterns
- Quality Rails compliance: All lint checks pass

Co-Authored-By: Claude Opus 4.5 <noreply@anthropic.com>

apps/api/src/brain/brain.controller.ts

@@ -1,6 +1,12 @@
 import { Controller, Get, Post, Body, Query, UseGuards } from "@nestjs/common";
 import { BrainService } from "./brain.service";
-import { BrainQueryDto, BrainContextDto } from "./dto";
+import { IntentClassificationService } from "./intent-classification.service";
+import {
+  BrainQueryDto,
+  BrainContextDto,
+  ClassifyIntentDto,
+  IntentClassificationResultDto,
+} from "./dto";
 import { AuthGuard } from "../auth/guards/auth.guard";
 import { WorkspaceGuard, PermissionGuard } from "../common/guards";
 import { Workspace, Permission, RequirePermission } from "../common/decorators";
@@ -13,7 +19,10 @@ import { Workspace, Permission, RequirePermission } from "../common/decorators";
 @Controller("brain")
 @UseGuards(AuthGuard, WorkspaceGuard, PermissionGuard)
 export class BrainController {
-  constructor(private readonly brainService: BrainService) {}
+  constructor(
+    private readonly brainService: BrainService,
+    private readonly intentClassificationService: IntentClassificationService
+  ) {}
 
   /**
    * @description Query workspace entities with flexible filtering options.
@@ -66,4 +75,18 @@ export class BrainController {
     const parsedLimit = limit ? Math.min(parseInt(limit, 10) || 20, 100) : 20;
     return this.brainService.search(workspaceId, searchTerm || "", parsedLimit);
   }
+
+  /**
+   * @description Classify a natural language query into a structured intent.
+   * Uses hybrid classification: rule-based (fast) with optional LLM fallback.
+   * @param dto - Classification request with query and optional useLlm flag
+   * @returns Intent classification with confidence, entities, and method used
+   * @throws UnauthorizedException if user lacks workspace access
+   * @throws ForbiddenException if user lacks required permissions
+   */
+  @Post("classify")
+  @RequirePermission(Permission.WORKSPACE_ANY)
+  async classifyIntent(@Body() dto: ClassifyIntentDto): Promise<IntentClassificationResultDto> {
+    return this.intentClassificationService.classify(dto.query, dto.useLlm);
+  }
 }