Add Docker packaging and migrate from better-sqlite3 to libsql

Docker self-hosting support:
- Dockerfile (multi-stage Alpine build with tini init)
- docker-compose.yml with named volume for SQLite persistence
- /api/health endpoint for container health checks
- Auto-migration on startup via drizzle-orm/libsql/migrator
- Graceful shutdown (SIGTERM stops scheduler, closes DB)
- Next.js standalone output mode for minimal image size

Database driver migration (better-sqlite3 → @libsql/client):
- Eliminates native C++ compilation, enabling Alpine Docker images
- All DB queries converted from sync to async across services and routes
- DATABASE_URL now uses libsql file: prefix format
- drizzle.config.ts dialect changed to turso for libsql support
- Initial migration files generated in drizzle/

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

CLAUDE.md

@@ -22,7 +22,7 @@ pnpm db:studio        # Open Drizzle Studio (visual DB browser)
 ### Stack
 
 - **Framework**: Next.js 16 (App Router), React 19, TypeScript
-- **Database**: SQLite via better-sqlite3 + Drizzle ORM (WAL mode, singleton via `globalThis`)
+- **Database**: SQLite via @libsql/client + Drizzle ORM (WAL mode, singleton via `globalThis`, async queries)
 - **Auth**: Better Auth with Drizzle adapter, email/password
 - **Styling**: Tailwind CSS v4, shadcn components, dark cinema theme with warm primary accents
 - **Fonts**: DM Serif Display (display), DM Sans (body), Geist Mono (mono)