feat(#2): Implement PostgreSQL 17 + pgvector database schema

Establishes multi-tenant database layer with vector similarity search for AI-powered memory features. Includes Docker infrastructure, Prisma ORM integration, NestJS services, and shared types across the monorepo.

Key changes:
- Docker: PostgreSQL 17 + pgvector v0.7.4, Valkey cache
- Schema: 8 models (User, Workspace, Task, Event, Project, ActivityLog, MemoryEmbedding) with RLS preparation
- NestJS: PrismaModule, DatabaseModule, EmbeddingsService
- Shared: Type-safe enums, constants, and database types

Fixes #2

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

apps/api/src/app.controller.ts

@@ -1,11 +1,15 @@
 import { Controller, Get } from "@nestjs/common";
 import { AppService } from "./app.service";
+import { PrismaService } from "./prisma/prisma.service";
 import type { ApiResponse, HealthStatus } from "@mosaic/shared";
 import { successResponse } from "@mosaic/shared";
 
 @Controller()
 export class AppController {
-  constructor(private readonly appService: AppService) {}
+  constructor(
+    private readonly appService: AppService,
+    private readonly prisma: PrismaService,
+  ) {}
 
   @Get()
   getHello(): string {
@@ -13,10 +17,25 @@ export class AppController {
   }
 
   @Get("health")
-  getHealth(): ApiResponse<HealthStatus> {
+  async getHealth(): Promise<ApiResponse<HealthStatus>> {
+    const dbHealthy = await this.prisma.isHealthy();
+    const dbInfo = await this.prisma.getConnectionInfo();
+
+    const overallStatus = dbHealthy ? "healthy" : "degraded";
+    const packageVersion = process.env.npm_package_version;
+
     return successResponse({
-      status: "healthy",
+      status: overallStatus,
       timestamp: new Date().toISOString(),
+      ...(packageVersion && { version: packageVersion }),
+      checks: {
+        database: {
+          status: dbHealthy ? "healthy" : "unhealthy",
+          message: dbInfo.connected
+            ? `Connected to ${dbInfo.database} (${dbInfo.version})`
+            : "Database connection failed",
+        },
+      },
     });
   }
 }