feat: sync /var/log for system log persistence

Co-Authored-By: Claude Opus 4.6 <noreply@anthropic.com>

entrypoint.py

@@ -32,7 +32,7 @@ PKG_FILE = os.path.join(PERSIST_PATH, "user-packages.list")
 PIP_FILE = os.path.join(PERSIST_PATH, "pip-packages.txt")
 
 # Directories to sync (user data only, no system binaries)
-SYNC_DIRS = ["/home", "/root", "/usr/local", "/opt", "/var/lib", "/etc"]
+SYNC_DIRS = ["/home", "/root", "/usr/local", "/opt", "/var/lib", "/var/log", "/etc"]
 
 # Exclude from rsync (relative paths — rsync matches from transfer root)
 RSYNC_EXCLUDES = ["*.sock", "*.pid", "*.lock"]