feat(database): add MySQL storage backend integration (#163)

[Nsuccess]

This PR implements MySQL database integration for MemU, enabling memory data synchronization with MySQL for import, export, and backup use cases.

Changes
New Files
MySQL Database Module (src/memu/database/mysql/):

init.py - Module entry point with build_mysql_database() factory
mysql.py - MySQLStore class implementing the Database interface
session.py - SessionManager for MySQL connection handling
schema.py - SQLAlchemy model generation and caching
models.py - SQLModel definitions for MySQL tables
migration.py - DDL management (create/validate modes)
Repository Layer (src/memu/database/mysql/repositories/):

base.py - MySQLRepoBase with JSON embedding serialization
resource_repo.py - Resource CRUD operations
memory_category_repo.py - Category CRUD operations
memory_item_repo.py - Memory item CRUD with vector search
category_item_repo.py - Category-item relationship management
Documentation:

docs/mysql-integration.md - Setup guide, configuration, usage examples
Tests:

tests/test_mysql.py - 17 unit tests covering all components
Modified Files
src/memu/app/settings.py - Added mysql to MetadataStoreConfig.provider literal
src/memu/database/factory.py - Added MySQL provider branch in build_database()
Implementation Details
Architecture
Follows the existing Postgres pattern for consistency
Uses SQLModel/SQLAlchemy for ORM
Embeddings stored as JSON TEXT (MySQL lacks native vector type)
Brute-force cosine similarity for vector search
Configuration
from memu.app.settings import DatabaseConfig, MetadataStoreConfig

config = DatabaseConfig(
metadata_store=MetadataStoreConfig(
provider="mysql",
dsn="mysql+pymysql://user:password@localhost:3306/memu_db",
)
)
Database Schema
Creates 4 tables: resources, memory_items, memory_categories, category_items

Testing
All 17 tests pass:

pytest tests/test_mysql.py -v
==================================== 17 passed ====================================
Checklist
Complete MySQL integration that can be run in practice
Vector storage support (via JSON serialization + local cosine search)
Documentation with setup and usage instructions
Unit tests for all components
No breaking changes to existing functionality
Closes #163

[ankaisen]

@Nsuccess Thanks for your PR! Could you please resolve the merge conflicts?

[Nsuccess]

@ankaisen Done! Merge conflicts resolved — Included both MySQL and SQLite providers.