[omnibox] Add fieldtrial testing config entry for OmniboxActiveSearchEngines

Also search engines page browser tests are updated.

Bug: 1213659
Change-Id: I633eff75a5deb7c8f7f65867879ae46e02317b39
Reviewed-on: https://chromium-review.googlesource.com/c/chromium/src/+/3453487
Reviewed-by: Justin Donnelly <jdonnelly@chromium.org>
Commit-Queue: Angela Yoeurng <yoangela@chromium.org>
Cr-Commit-Position: refs/heads/main@{#969743}

chrome/test/data/webui/settings/search_engines_page_test.ts

@@ -157,6 +157,7 @@ suite('SearchEngineEntryTests', function() {
     document.body.innerHTML = '';
     entry = document.createElement('settings-search-engine-entry');
     entry.set('engine', searchEngine);
+    entry.set('isActiveSearchEnginesFlagEnabled', false);
     document.body.appendChild(entry);
   });
 
@@ -446,6 +447,7 @@ suite('SearchEnginePageTests', function() {
       others: searchEnginesInfo.others.slice(),
       extensions: searchEnginesInfo.extensions.slice(),
     });
+    loadTimeData.overrideValues({'isActiveSearchEnginesFlagEnabled': false});
     SearchEnginesBrowserProxyImpl.setInstance(browserProxy);
     document.body.innerHTML = '';
     page = document.createElement('settings-search-engines-page');

testing/variations/fieldtrial_testing_config.json

@@ -4120,6 +4120,24 @@
             ]
         }
     ],
+    "OmniboxActiveSearchEngines": [
+        {
+            "platforms": [
+                "chromeos",
+                "linux",
+                "mac",
+                "windows"
+            ],
+            "experiments": [
+                {
+                    "name": "Enabled",
+                    "enable_features": [
+                        "OmniboxActiveSearchEngines"
+                    ]
+                }
+            ]
+        }
+    ],
     "OmniboxBundledExperimentV1": [
         {
             "platforms": [