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/calendar.rs

@@ -665,7 +665,6 @@ impl CalDAVClient {
         }
 
         let body = response.text().await.map_err(CalDAVError::RequestError)?;
-        println!("Discovery response for {}: {}", path, body);
 
         let mut calendar_paths = Vec::new();
 
@@ -676,7 +675,6 @@ impl CalDAVClient {
 
                 // Extract href first
                 if let Some(href) = self.extract_xml_content(response_content, "href") {
-                    println!("🔍 Checking resource: {}", href);
 
                     // Check if this is a calendar collection by looking for supported-calendar-component-set
                     // This indicates it's an actual calendar that can contain events
@@ -700,14 +698,10 @@ impl CalDAVClient {
                             && !href.ends_with("/calendars/")
                             && href.ends_with('/')
                         {
-                            println!("📅 Found calendar collection: {}", href);
                             calendar_paths.push(href);
                         } else {
-                            println!("❌ Skipping system/root directory: {}", href);
                         }
                     } else {
-                        println!("ℹ️  Not a calendar collection: {} (is_calendar: {}, has_collection: {})", 
-                               href, is_calendar, has_collection);
                     }
                 }
             }