Remove remaining verbose CalDAV discovery and authentication logs

- Remove discovery response XML dumps that flood console
- Remove calendar collection checking logs
- Remove authentication success messages
- Remove API call password length logging
- Fix unused variable warning

Backend now runs with minimal essential logging only.

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

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

backend/src/handlers/auth.rs

@@ -82,10 +82,6 @@ pub async fn get_user_info(
         .await
         .map_err(|e| ApiError::Internal(format!("Failed to discover calendars: {}", e)))?;
 
-    println!(
-        "✅ Authentication successful! Found {} calendars",
-        calendar_paths.len()
-    );
 
     let calendars: Vec<CalendarInfo> = calendar_paths
         .iter()