🔍 Update how shared preferences are handled by the widget

chrome/android/java/AndroidManifest.xml

Index: chrome/android/java/AndroidManifest.xml
diff --git a/chrome/android/java/AndroidManifest.xml b/chrome/android/java/AndroidManifest.xml
index a528f07bc9a6239efcf79793098e918a2eeffe01..dbaecfc48459aeaa7f98c86e8b5b7ba6dfca7675 100644
--- a/chrome/android/java/AndroidManifest.xml
+++ b/chrome/android/java/AndroidManifest.xml
@@ -731,8 +731,7 @@ by a child template that "extends" this file.
 
         {% if channel in ['canary', 'default'] %}
         <!-- Search widget -->
-        <receiver android:name="org.chromium.chrome.browser.searchwidget.SearchWidgetProvider"
-            android:process=":search_widget">
+        <receiver android:name="org.chromium.chrome.browser.searchwidget.SearchWidgetProvider">
             <intent-filter>
                 <action android:name="android.appwidget.action.APPWIDGET_UPDATE" />
             </intent-filter>
@@ -748,7 +747,7 @@ by a child template that "extends" this file.
 
         <!-- Search Activity -->
         <activity android:name="org.chromium.chrome.browser.searchwidget.SearchActivity"
-            android:theme="@style/MainTheme"
+            android:theme="@style/SearchActivityTheme"
             android:label="Search"
             android:exported="false"
             android:launchMode="singleTask"