Search widget: Set color scheme to use material design (#29569)

The search widget needs to have better alignment with Material colors.
It is important for it to feel like it is integrated to the OS.
Resolves: https://github.com/brave/brave-browser/issues/46537

android/java/res/values-night/brave_colors.xml

@@ -2,7 +2,7 @@
 <!-- Copyright (c) 2019 The Brave Authors. All rights reserved.
      This Source Code Form is subject to the terms of the Mozilla Public
      License, v. 2.0. If a copy of the MPL was not distributed with this file,
-     You can obtain one at http://mozilla.org/MPL/2.0/
+     You can obtain one at https://mozilla.org/MPL/2.0/.
 -->
 
 <resources>
@@ -170,8 +170,6 @@
     <color name="brave_wallet_dapp_text_color">@android:color/white</color>
 
     <!-- Quick Action Search and Bookmark Widget -->
-    <color name="quick_action_search_and_bookmark_widget_bg_color">#F21E2029</color>
-    <color name="quick_action_search_and_bookmark_widget_search_bg_color">#405E6175</color>
     <color name="quick_action_search_and_bookmark_widget_bookmark_bg_color">#FFFFFF</color>
     <color name="quick_action_search_and_bookmark_widget_tint">#F0F2FF</color>
     <color name="quick_action_search_and_bookmark_widget_text_color">#CED0DB</color>