[fenix] For https://github.com/mozilla-mobile/fenix/issues/22034: Inactive tabs prompt is redisplayed after dismissing by turning on Auto close

app/src/main/java/org/mozilla/fenix/tabstray/browser/InactiveTabsAutoCloseDialogController.kt

@@ -20,7 +20,7 @@ class InactiveTabsAutoCloseDialogController(
      * Dismiss the auto-close dialog.
      */
     fun close() {
-        settings.hasInactiveTabsAutoCloseDialogBeenDismissed = true
+        markDialogAsShown()
         refeshInactiveTabsSecion()
     }
 
@@ -28,7 +28,7 @@ class InactiveTabsAutoCloseDialogController(
      * Enable the auto-close feature with the after a month setting.
      */
     fun enableAutoClosed() {
-        settings.hasInactiveTabsAutoCloseDialogBeenDismissed = true
+        markDialogAsShown()
         settings.closeTabsAfterOneMonth = true
         settings.closeTabsAfterOneWeek = false
         settings.closeTabsAfterOneDay = false
@@ -36,6 +36,13 @@ class InactiveTabsAutoCloseDialogController(
         refeshInactiveTabsSecion()
     }
 
+    /**
+     * Marks the dialog as shown and to not be displayed again.
+     */
+    private fun markDialogAsShown() {
+        settings.hasInactiveTabsAutoCloseDialogBeenDismissed = true
+    }
+
     @VisibleForTesting
     internal fun refeshInactiveTabsSecion() {
         val tabs = browserStore.state.tabs.filter(tabFilter)