Refactor handlers.rs into modular structure for better maintainability

- Split 1921-line handlers.rs into focused modules:
  - handlers/auth.rs: Authentication handlers (login, verify_token, get_user_info)
  - handlers/calendar.rs: Calendar management (create_calendar, delete_calendar)
  - handlers/events.rs: Event operations (CRUD operations, fetch events)
  - handlers/series.rs: Event series operations (recurring events management)
- Main handlers.rs now serves as clean re-export module
- All tests passing (14 integration + 7 unit + 3 doc tests)
- Maintains backward compatibility with existing API routes
- Improves code organization and separation of concerns

🤖 Generated with [Claude Code](https://claude.ai/code)

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

backend/src/auth.rs

@@ -104,7 +104,7 @@ impl AuthService {
         Ok(())
     }
 
-    fn generate_token(&self, username: &str, server_url: &str) -> Result<String, ApiError> {
+    pub fn generate_token(&self, username: &str, server_url: &str) -> Result<String, ApiError> {
         let now = Utc::now();
         let expires_at = now + Duration::hours(24); // Token valid for 24 hours