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/prisma/prisma.module.ts

@@ -0,0 +1,13 @@
+import { Global, Module } from "@nestjs/common";
+import { PrismaService } from "./prisma.service";
+
+/**
+ * Global Prisma module providing database access throughout the application
+ * Marked as @Global() so PrismaService is available in all modules without importing
+ */
+@Global()
+@Module({
+  providers: [PrismaService],
+  exports: [PrismaService],
+})
+export class PrismaModule {}

apps/api/src/prisma/prisma.service.ts

@@ -0,0 +1,95 @@
+import {
+  Injectable,
+  Logger,
+  OnModuleDestroy,
+  OnModuleInit,
+} from "@nestjs/common";
+import { PrismaClient } from "@prisma/client";
+
+/**
+ * Prisma service that manages database connection lifecycle
+ * Extends PrismaClient to provide connection management and health checks
+ */
+@Injectable()
+export class PrismaService
+  extends PrismaClient
+  implements OnModuleInit, OnModuleDestroy
+{
+  private readonly logger = new Logger(PrismaService.name);
+
+  constructor() {
+    super({
+      log:
+        process.env.NODE_ENV === "development"
+          ? ["query", "info", "warn", "error"]
+          : ["error"],
+    });
+  }
+
+  /**
+   * Connect to database when NestJS module initializes
+   */
+  async onModuleInit() {
+    try {
+      await this.$connect();
+      this.logger.log("Database connection established");
+    } catch (error) {
+      this.logger.error("Failed to connect to database", error);
+      throw error;
+    }
+  }
+
+  /**
+   * Disconnect from database when NestJS module is destroyed
+   */
+  async onModuleDestroy() {
+    await this.$disconnect();
+    this.logger.log("Database connection closed");
+  }
+
+  /**
+   * Health check for database connectivity
+   * @returns true if database is accessible, false otherwise
+   */
+  async isHealthy(): Promise<boolean> {
+    try {
+      await this.$queryRaw`SELECT 1`;
+      return true;
+    } catch (error) {
+      this.logger.error("Database health check failed", error);
+      return false;
+    }
+  }
+
+  /**
+   * Get database connection info for debugging
+   * @returns Connection status and basic info
+   */
+  async getConnectionInfo(): Promise<{
+    connected: boolean;
+    database?: string;
+    version?: string;
+  }> {
+    try {
+      const result = await this.$queryRaw<
+        Array<{ current_database: string; version: string }>
+      >`
+        SELECT current_database(), version()
+      `;
+
+      if (result && result.length > 0 && result[0]) {
+        const dbVersion = result[0].version?.split(" ")[0];
+        return {
+          connected: true,
+          database: result[0].current_database,
+          ...(dbVersion && { version: dbVersion }),
+        };
+      }
+
+      return { connected: false };
+    } catch (error) {
+      this.logger.error("Failed to get connection info", error);
+      return { connected: false };
+    }
+  }
+}