feat: implement background process logging and cleanup

- Add persistent logging for backgrounded shell processes in ~/.gemini/tmp/background-processes
- Implement automatic cleanup of background logs older than 7 days on CLI startup
- Support real-time output syncing to log files for both PTY and child_process execution
- Update UI to indicate log file availability for background tasks
- Add comprehensive unit and integration tests for logging and cleanup logic

packages/cli/src/ui/contexts/UIActionsContext.tsx

@@ -76,7 +76,7 @@ export interface UIActions {
   revealCleanUiDetailsTemporarily: (durationMs?: number) => void;
   handleWarning: (message: string) => void;
   setEmbeddedShellFocused: (value: boolean) => void;
-  dismissBackgroundShell: (pid: number) => void;
+  dismissBackgroundShell: (pid: number) => Promise<void>;
   setActiveBackgroundShellPid: (pid: number) => void;
   setIsBackgroundShellListOpen: (isOpen: boolean) => void;
   setAuthContext: (context: { requiresRestart?: boolean }) => void;