feat: implement Phase 1 Foundation for AutoScheduler GTD System

- Initialize npm workspaces monorepo (backend, frontend, shared-types)
- Scaffold NestJS backend with modules: Auth, Users, Tasks, Projects, Inbox, Health
- Create React frontend with Vite, TailwindCSS, Radix UI
- Implement TypeORM entities: User, InboxItem, Task, Project
- Add JWT authentication with Passport.js and bcrypt
- Build Inbox capture API (POST /inbox, GET /inbox, POST /inbox/:id/process)
- Create Inbox UI with quick-add form and GTD processing workflow modal
- Configure Docker Compose stack (postgres, redis, backend, frontend)
- Add health check endpoint with database/Redis status
- Write unit tests for auth and inbox services

Phase 1 features complete:
- GTD Inbox Capture: Manual tasks via web form quick-add
- GTD Processing Workflow: Interactive inbox processing interface

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

packages/backend/src/modules/health/health.service.ts

@@ -0,0 +1,67 @@
+import { Injectable, Logger } from '@nestjs/common';
+import { DataSource } from 'typeorm';
+import { ConfigService } from '@nestjs/config';
+import Redis from 'ioredis';
+import type { HealthCheckResponseDto } from '@nick-tracker/shared-types';
+
+@Injectable()
+export class HealthService {
+  private readonly logger = new Logger(HealthService.name);
+  private redis: Redis | null = null;
+
+  constructor(
+    private readonly dataSource: DataSource,
+    private readonly configService: ConfigService,
+  ) {
+    this.initRedis();
+  }
+
+  private initRedis() {
+    const redisUrl = this.configService.get<string>('REDIS_URL');
+    if (redisUrl) {
+      try {
+        this.redis = new Redis(redisUrl);
+      } catch (error) {
+        this.logger.warn('Failed to connect to Redis:', error);
+      }
+    }
+  }
+
+  async check(): Promise<HealthCheckResponseDto> {
+    const dbStatus = await this.checkDatabase();
+    const redisStatus = await this.checkRedis();
+
+    return {
+      status: dbStatus === 'connected' && redisStatus === 'connected' ? 'ok' : 'error',
+      database: dbStatus,
+      redis: redisStatus,
+    };
+  }
+
+  private async checkDatabase(): Promise<'connected' | 'disconnected'> {
+    try {
+      if (this.dataSource.isInitialized) {
+        await this.dataSource.query('SELECT 1');
+        return 'connected';
+      }
+      return 'disconnected';
+    } catch (error) {
+      this.logger.warn('Database health check failed:', error);
+      return 'disconnected';
+    }
+  }
+
+  private async checkRedis(): Promise<'connected' | 'disconnected'> {
+    if (!this.redis) {
+      return 'disconnected';
+    }
+
+    try {
+      const result = await this.redis.ping();
+      return result === 'PONG' ? 'connected' : 'disconnected';
+    } catch (error) {
+      this.logger.warn('Redis health check failed:', error);
+      return 'disconnected';
+    }
+  }
+}