For #12544 - Prevent search engines mixup

Stricter synchronization by always using the same "loadedSearchEngines"
variable.
With "loadedSearchEngines" calling "refreshAsync()" we also get the fallback
engines to contain reddit and youtube (which are programatically added) and
also now we properly remember and display the engines added by user.

app/src/main/java/org/mozilla/fenix/components/searchengine/FenixSearchEngineProvider.kt

@@ -7,7 +7,6 @@ package org.mozilla.fenix.components.searchengine
 import android.content.Context
 import androidx.annotation.VisibleForTesting
 import kotlinx.coroutines.CoroutineScope
-import kotlinx.coroutines.Deferred
 import kotlinx.coroutines.Dispatchers
 import kotlinx.coroutines.Job
 import kotlinx.coroutines.async
@@ -33,14 +32,16 @@ import java.util.Locale
 open class FenixSearchEngineProvider(
     private val context: Context
 ) : SearchEngineProvider, CoroutineScope by CoroutineScope(Job() + Dispatchers.IO) {
-    private val locationService: LocationService = if (Config.channel.isDebug) {
-        LocationService.dummy()
-    } else {
-        MozillaLocationService(
-            context,
-            context.components.core.client,
-            BuildConfig.MLS_TOKEN
-        )
+    private val locationService = with(MozillaLocationService(
+        context,
+        context.components.core.client,
+        BuildConfig.MLS_TOKEN
+    )) {
+        if (Config.channel.isDebug || !this.hasRegionCached()) {
+            LocationService.dummy()
+        } else {
+            this
+        }
     }
 
     // We have two search engine types: one based on MLS reported region, one based only on Locale.
@@ -93,17 +94,6 @@ open class FenixSearchEngineProvider(
 
     private var loadedSearchEngines = refreshAsync()
 
-    // https://github.com/mozilla-mobile/fenix/issues/9935
-    // Create new getter that will return the fallback SearchEngineList if
-    // the main one hasn't completed yet
-    private val searchEngines: Deferred<SearchEngineList>
-        get() =
-            if (isRegionCachedByLocationService) {
-                loadedSearchEngines
-            } else {
-                fallbackEngines
-            }
-
     fun getDefaultEngine(context: Context): SearchEngine {
         val engines = installedSearchEngines(context)
         val selectedName = context.settings().defaultSearchEngineName
@@ -117,7 +107,7 @@ open class FenixSearchEngineProvider(
      */
     fun installedSearchEngines(context: Context): SearchEngineList = runBlocking {
         val installedIdentifiers = installedSearchEngineIdentifiers(context)
-        val engineList = searchEngines.await()
+        val engineList = loadedSearchEngines.await()
 
         engineList.copy(
             list = engineList.list.filter {
@@ -188,7 +178,11 @@ open class FenixSearchEngineProvider(
     }
 
     private fun refreshAsync() = async {
-        val engineList = baseSearchEngines.await()
+        val engineList = if (isRegionCachedByLocationService) {
+            baseSearchEngines.await()
+        } else {
+            fallbackEngines.await()
+        }
         val bundledList = bundledSearchEngines.await().list
         val customList = customSearchEngines.await().list