refactor: reorganize to standard PHP structure

- Moved /lib → /src (PHP source code)
- Moved /includes → /public/includes (main site templates)
- Admin section remains self-contained in /public/admin with its own /inc
- Updated all require/include paths across codebase
- Updated config/bootstrap.php, justfile, tests, docs
- All tests passing ✅

Structure now follows PHP best practices:
  /config      - Configuration files
  /database    - SQLite database + schema
  /docs        - Documentation (intact)
  /nginx       - Server config (intact)
  /public      - Web-accessible files (entry point)
    /admin     - Self-contained admin interface
    /assets    - CSS, fonts, icons
    /includes  - Main site templates (header/footer)
  /scripts     - Deployment scripts (intact)
  /src         - PHP source classes (Database, AdminAuth, RateLimit)
  /tests       - Test suites

docs/MIGRATION_GUIDE.md

@@ -66,7 +66,7 @@ git commit -m "Pre-migration checkpoint"
 This will:
 - Move `apps/public/*` to root
 - Move `apps/admin/` to `admin/`
-- Rename `shared/` to `lib/`
+- Rename `shared/` to `src/`
 - Update all `require` paths automatically
 - Remove `apps/` directory
 - Update `.gitignore`
@@ -149,9 +149,9 @@ just deploy-admin
 | `apps/public/assets/` | `assets/` |
 | `apps/public/inc/` | `inc/` |
 | `apps/admin/` | `admin/` |
-| `shared/Database.php` | `lib/Database.php` |
-| `shared/config.php` | `lib/config.php` |
-| `shared/cache/` | `lib/cache/` |
+| `shared/Database.php` | `src/Database.php` |
+| `shared/config.php` | `src/config.php` |
+| `shared/cache/` | `src/cache/` |
 
 ### Path Updates