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>

docker/postgres/Dockerfile

@@ -0,0 +1,25 @@
+FROM postgres:17-alpine
+
+LABEL maintainer="Mosaic Stack <dev@mosaic.local>"
+LABEL description="PostgreSQL 17 with pgvector extension"
+
+# Install build dependencies for pgvector
+RUN apk add --no-cache --virtual .build-deps \
+    git \
+    build-base
+
+# Clone and build pgvector v0.7.4 (without LLVM bitcode compilation)
+RUN git clone --branch v0.7.4 https://github.com/pgvector/pgvector.git /tmp/pgvector \
+    && cd /tmp/pgvector \
+    && make OPTFLAGS="" with_llvm=no \
+    && make install with_llvm=no \
+    && rm -rf /tmp/pgvector
+
+# Clean up build dependencies to reduce image size
+RUN apk del .build-deps
+
+# Copy initialization scripts
+COPY init-scripts/ /docker-entrypoint-initdb.d/
+
+# Expose PostgreSQL port
+EXPOSE 5432

docker/postgres/init-scripts/00-init.sql

@@ -0,0 +1,18 @@
+-- Mosaic Stack Database Initialization Script
+-- This script runs automatically when the PostgreSQL container is first created
+
+-- Enable UUID extension for UUID generation
+CREATE EXTENSION IF NOT EXISTS "uuid-ossp";
+
+-- Enable pgvector extension for vector similarity search
+CREATE EXTENSION IF NOT EXISTS "vector";
+
+-- Set default timezone to UTC
+SET timezone = 'UTC';
+
+-- Log successful initialization
+DO $$
+BEGIN
+  RAISE NOTICE 'Mosaic Stack database initialized successfully';
+  RAISE NOTICE 'Extensions enabled: uuid-ossp, vector';
+END $$;