feat: Implement search filter persistence and UI synchronization

src/ui_manager.py

@@ -686,6 +686,19 @@ class UIManager:
         # Pack after file_info so it appears to the left of it
         self.last_backup_label.pack(side=tk.RIGHT)
 
+        # Tiny filter activity hint (right side, left of backup info)
+        self.filter_hint_label = tk.Label(
+            self.status_bar,
+            text="",
+            anchor=tk.E,
+            font=("TkDefaultFont", 9),
+            padx=8,
+            pady=2,
+            bg=theme_colors["bg"],
+            fg="#6c757d",
+        )
+        self.filter_hint_label.pack(side=tk.RIGHT)
+
         return self.status_bar
 
     def update_last_backup(self, when_text: str) -> None:
@@ -815,6 +828,18 @@ class UIManager:
             # Non-fatal UI convenience; ignore errors
             pass
 
+    def set_filter_hint(self, active: bool, text: str | None = None) -> None:
+        """Show or hide a small status hint when filters are active.
+
+        Args:
+            active: Whether filters are currently active
+            text: Optional custom hint text (defaults to 'Filters active')
+        """
+        if not self.filter_hint_label:
+            return
+        hint_text = (text or "Filters active") if active else ""
+        self.filter_hint_label.config(text=hint_text)
+
     def create_edit_window(
         self, values: tuple[str, ...], callbacks: dict[str, Callable]
     ) -> tk.Toplevel: