feat: implement timezone-aware logging system

- Fix inconsistent timestamp formats in logs for easier troubleshooting
- All logging systems now respect Docker TZ environment variable (e.g., TZ=America/New_York)
- Add TimezoneAwareFormatter for Python's standard logging module
- Enhance _log function with robust timezone support and fallbacks
- Replace placeholder logging functions with centralized core.logging._log
- Support both zoneinfo (Python 3.9+) and pytz (older versions)
- Users now see consistent timezone formatting across all log outputs

SUMMARY.md

@@ -210,6 +210,45 @@ Preserve movie and TV import dates in Emby/Jellyfin/Plex by preventing upgraded
 
 ---
 
-**Last Updated:** September 13, 2025  
-**Version:** v0.6.3-dev  
+### 🆕 v0.6.4 Timezone-Aware Logging Fix (September 2025)
+
+**🕰️ Universal Timezone Consistency:**
+- **Problem**: Mixed timestamp formats in logs made troubleshooting difficult
+  - Some logs: `[2025-09-14T09:37:00.338045]` (local time without timezone info)
+  - Other logs: `[2025-09-14T13:37:00+00:00]` (UTC with timezone info)
+  - Docker `TZ=America/New_York` environment variable not respected by all logging systems
+
+**⚡ Comprehensive Logging Fix:**
+- **Unified Timezone Handling**: All logging systems now respect the `TZ` environment variable
+- **Custom TimezoneAwareFormatter**: Python's standard logging now uses container timezone
+- **Enhanced _log Function**: Custom logging function updated with robust timezone support
+- **Centralized Logging**: Replaced placeholder logging functions with consistent implementation
+
+**🔧 Technical Implementation:**
+- **New Class**: `TimezoneAwareFormatter` for Python's standard logging module
+- **Enhanced Function**: `_get_local_timezone()` with fallbacks for different Python versions
+- **Cross-Compatibility**: Supports both `zoneinfo` (Python 3.9+) and `pytz` (older versions)
+- **Consistent Import**: All client modules now use centralized `core.logging._log`
+
+**🏆 User Experience Improvements:**
+- **Consistent Timestamps**: All logs now show the same timezone format
+- **Easier Troubleshooting**: Timestamps match user's local environment
+- **No More Confusion**: No need to mentally convert between UTC and local time
+- **Production Ready**: Robust fallbacks ensure logging works in all environments
+
+**📋 Before/After Example:**
+```
+# Before (Inconsistent)
+sonarr-nfo-cache  | [2025-09-14T09:37:00.338045] DEBUG: Mapped Radarr path...
+sonarr-nfo-cache  | [2025-09-14T13:37:00+00:00] INFO: Batched movie webhook...
+
+# After (Consistent)  
+sonarr-nfo-cache  | [2025-09-14T09:37:00-04:00] DEBUG: Mapped Radarr path...
+sonarr-nfo-cache  | [2025-09-14T09:37:00-04:00] INFO: Batched movie webhook...
+```
+
+---
+
+**Last Updated:** September 14, 2025  
+**Version:** v0.6.4-dev  
 **Status:** Enhanced Production Ready