[fenix] Use new async API to load and access search engines

Use the new asynchronous features of the search engine
manager from a-c to avoid the latency required to load
the default search engine.

app/src/main/java/org/mozilla/fenix/components/Search.kt

@@ -31,12 +31,11 @@ class Search(private val context: Context) {
         ).apply {
             registerForLocaleUpdates(context)
             GlobalScope.launch {
-                loadAsync(context).await()
+                defaultSearchEngine = getDefaultSearchEngineAsync(
+                    context,
+                    Settings.getInstance(context).defaultSearchEngineName
+                )
             }
-            defaultSearchEngine = getDefaultSearchEngine(
-                context,
-                Settings.getInstance(context).defaultSearchEngineName
-            )
         }
     }
 }

app/src/main/java/org/mozilla/fenix/search/awesomebar/AwesomeBarView.kt

@@ -152,9 +152,8 @@ class AwesomeBarView(
 
             defaultSearchSuggestionProvider =
                 SearchSuggestionProvider(
-                    searchEngine = components.search.searchEngineManager.getDefaultSearchEngine(
-                        this
-                    ),
+                    context = this,
+                    searchEngineManager = components.search.searchEngineManager,
                     searchUseCase = searchUseCase,
                     fetchClient = components.core.client,
                     mode = SearchSuggestionProvider.Mode.MULTIPLE_SUGGESTIONS,