Extract Edit menu logic from BrowserContainerViewController

It is planned to add more entries with the menu, and the logic to handle
it will grow accordingly.
Extract the logic to a new class and add a flag to use the
buildMenuWithBuilder API instead of the setMenuItems: API.

Bug: 1414726
Change-Id: I8e4fb40c4331eda8791155bf0b650967afc69091
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/4238880
Commit-Queue: Olivier Robin <[email protected]>
Reviewed-by: Sebastien Seguin-Gagnon <[email protected]>
Reviewed-by: Mark Cogan <[email protected]>
Cr-Commit-Position: refs/heads/main@{#1106320}
diff --git a/ios/chrome/browser/flags/about_flags.mm b/ios/chrome/browser/flags/about_flags.mm
index 4f21ec6..74ca318 100644
--- a/ios/chrome/browser/flags/about_flags.mm
+++ b/ios/chrome/browser/flags/about_flags.mm
@@ -1359,6 +1359,10 @@
      flag_descriptions::kIOSEditMenuPartialTranslateName,
      flag_descriptions::kIOSEditMenuPartialTranslateDescription,
      flags_ui::kOsIos, FEATURE_VALUE_TYPE(kIOSEditMenuPartialTranslate)},
+    {"ios-custom-browser-edit-menu",
+     flag_descriptions::kIOSCustomBrowserEditMenuName,
+     flag_descriptions::kIOSCustomBrowserEditMenuDescription, flags_ui::kOsIos,
+     FEATURE_VALUE_TYPE(kIOSCustomBrowserEditMenu)},
 };
 
 bool SkipConditionalFeatureEntry(const flags_ui::FeatureEntry& entry) {