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>

docs/scratchpads/2-postgresql-pgvector-schema.md

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+# Issue #2: PostgreSQL 17 + pgvector Schema
+
+## Objective
+Design and implement the PostgreSQL 17 database schema with pgvector extension for Mosaic Stack.
+
+## Approach
+1. **Docker Infrastructure** - Build PostgreSQL 17 container with pgvector extension
+2. **Prisma ORM** - Define schema with 8 core models (User, Workspace, Task, Event, Project, etc.)
+3. **Multi-tenant Design** - All tables indexed by workspace_id for RLS preparation
+4. **Vector Embeddings** - pgvector integration for semantic memory with HNSW index
+5. **NestJS Integration** - PrismaService + EmbeddingsService for database operations
+
+## Progress
+- [x] Plan approved
+- [x] Phase 1: Docker Setup (5 tasks) - COMPLETED
+- [x] Phase 2: Prisma Schema (5 tasks) - COMPLETED
+- [x] Phase 3: NestJS Integration (5 tasks) - COMPLETED
+- [x] Phase 4: Shared Types & Seed (5 tasks) - COMPLETED
+- [x] Phase 5: Build & Verification (2 tasks) - COMPLETED
+
+## Completion Summary
+**Issue #2 successfully completed on 2026-01-28**
+
+### What Was Delivered
+1. **Docker Infrastructure**
+   - PostgreSQL 17 with pgvector v0.7.4 (HNSW index enabled)
+   - Valkey for caching
+   - Custom Dockerfile building pgvector from source
+   - Init scripts for extension setup
+
+2. **Database Schema (Prisma)**
+   - 8 models: User, Workspace, WorkspaceMember, Task, Event, Project, ActivityLog, MemoryEmbedding
+   - 6 enums for type safety
+   - UUID primary keys throughout
+   - HNSW index on memory_embeddings for vector similarity search
+   - Full multi-tenant support with workspace_id indexing
+   - 2 migrations: init + vector index
+
+3. **NestJS Integration**
+   - PrismaModule (global)
+   - PrismaService with lifecycle hooks and health checks
+   - EmbeddingsService for pgvector operations (raw SQL)
+   - Health endpoint updated with database status
+
+4. **Shared Types**
+   - Enums mirroring Prisma schema
+   - Entity interfaces for type safety across monorepo
+   - Exported from @mosaic/shared
+
+5. **Development Tools**
+   - Seed script with sample data (user, workspace, project, tasks, event)
+   - Prisma scripts in package.json
+   - Turbo integration for prisma:generate
+   - All builds passing with strict TypeScript
+
+### Database Statistics
+- Tables: 8
+- Extensions: uuid-ossp, vector (pgvector 0.7.4)
+- Indexes: 14 total (including 1 HNSW vector index)
+- Seed data: 1 user, 1 workspace, 1 project, 5 tasks, 1 event
+
+## Testing
+- Unit tests for PrismaService (connection lifecycle, health check)
+- Unit tests for EmbeddingsService (store, search, delete operations)
+- Integration test with actual PostgreSQL database
+- Seed data validation via Prisma Studio
+
+## Notes
+### Design Decisions
+- **UUID primary keys** for multi-tenant scalability
+- **Native Prisma enums** mapped to PostgreSQL enums for type safety
+- **`Unsupported("vector(1536)")`** type for pgvector (raw SQL operations)
+- **Composite PK** for WorkspaceMember (workspaceId + userId)
+- **Self-referencing Task** model for subtasks support
+
+### Key Relations
+- User → ownedWorkspaces (1:N), workspaceMemberships (N:M via WorkspaceMember)
+- Workspace → tasks, events, projects, activityLogs, memoryEmbeddings (1:N each)
+- Task → subtasks (self-referencing), project (optional N:1)
+
+### RLS Preparation (M2 Milestone)
+- All tenant tables have workspace_id with index
+- Future: PostgreSQL session variables (app.current_workspace_id, app.current_user_id)
+- Future: RLS policies for workspace isolation