[Android] Move BottomToolbar code to brave-core (stage 1)

Moved code deleted in Chromium to brave-core

Chromium change:
https://chromium.googlesource.com/chromium/src.git/+/ad4cf0623574d9d7ea517d0063cb054d98766964

Duet: Clean up unused classes and resources

Delete all the classes and resources left unused by
Duet (BottomToolbar).

Bug: 1081343

android/brave_java_resources.gni

@@ -690,6 +690,11 @@ brave_java_resources = [
   "java/res/layout/binance_spinner_dropdown_item.xml",
   "java/res/layout/binance_spinner_item.xml",
   "java/res/layout/binance_summary_item.xml",
+  "java/res/layout/bottom_toolbar.xml",
+  "java/res/layout/bottom_toolbar_browsing.xml",
+  "java/res/layout/bottom_toolbar_menu_button.xml",
+  "java/res/layout/bottom_toolbar_tab_switcher.xml",
+  "java/res/layout/icon_row_menu_footer.xml",
   "java/res/layout/brave_ads_existing_user_dialog_layout.xml",
   "java/res/layout/brave_ads_new_user_dialog_layout.xml",
   "java/res/layout/brave_bookmark_toolbar.xml",
@@ -756,6 +761,7 @@ brave_java_resources = [
   "java/res/layout/ntp_widget_list_item_layout.xml",
   "java/res/layout/qa_code_check.xml",
   "java/res/layout/report_broken_site_layout.xml",
+  "java/res/layout/toolbar_space.xml",
   "java/res/layout/top_sites_layout.xml",
   "java/res/layout/tracker_item_layout.xml",
   "java/res/layout/user_wallet_activity.xml",