An explanation on how to implement a standard Android search interface with Fragment(s) in SingleActivity pattern. N/B: Some code snippets contains AndroidX's navigation component codes that might not be useful to your project(as you could be handling your fragment navigation differently)

AndroidManifest.xml

<?xml version="1.0" encoding="utf-8"?>
<manifest ...>
	<application ...>
		<!-- launchMode=singleTop is IMPORTANT to avoid relaunching MainActivity every time search is initiated -->
		<activity
			android:name=".MainActivity"
			android:launchMode="singleTop">
			<intent-filter>
				<action android:name="android.intent.action.MAIN" />
				<action android:name="android.intent.action.SEARCH" />

				<category android:name="android.intent.category.LAUNCHER" />
			</intent-filter>
			<meta-data
				android:name="android.app.searchable"
				android:resource="@xml/searchable" />
		</activity>
	</application>
</manifest>

list_menu.xml

<menu ...>
  <item
		android:id="@+id/menu_list_search"
		android:icon="@drawable/ic_action_search"
		android:orderInCategory="1"
		android:title="Search"
		app:showAsAction="ifRoom" />
</menu>

MainActivity.kt

class MainActivity : AppCompatActivity() {

    private lateinit var binding: MainActivityBinding

    private val navController: NavController by lazy {
        findNavController(R.id.navigation_host)
    }

    override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)
        binding = MainActivityBinding.inflate(layoutInflater)
        setContentView(binding.root)

        handleIntent(intent)
    }

    override fun onNewIntent(intent: Intent) {
        super.onNewIntent(intent)
        setIntent(intent)
        handleIntent(intent)
    }

    override fun onOptionsItemSelected(item: MenuItem): Boolean =
        item.onNavDestinationSelected(navController) || super.onOptionsItemSelected(item)

    override fun onSearchRequested(): Boolean {
      val customAppData = Bundle().apply{
      putString("key1", "value1")
      }
        startSearch(null, false, customAppData, false)
        return true
//        return super.onSearchRequested() // Use when there is no need to send custom app data
    }

    private fun handleIntent(intent: Intent) {
        // Verify the action and get the query
        if (Intent.ACTION_SEARCH == intent.action) {
            val query = intent.getStringExtra(SearchManager.QUERY) ?: return
						// Pass the [query] received to a fragment in which actual data-searching process will be done
						val navOptions = NavOptions.Builder().setLaunchSingleTop(true).build()
						navController.navigate(R.id.dest_search_results, SearchResultsFragmentArgs(query=query).toBundle(), navOptions)
        }
    }
}

searchable.xml

<?xml version="1.0" encoding="utf-8"?>
<searchable xmlns:android="http://schemas.android.com/apk/res/android"
	android:hint="@string/search_hint"
	android:label="@string/app_name"/>

SearchInitiatorFragment.kt

class SearchInitiatorFragment: Fragment(){
	override fun onCreate(savedInstanceState: Bundle?) {
        super.onCreate(savedInstanceState)

				// Needed to help show options menu from fragments
        setHasOptionsMenu(true)
    }
	
	override fun onCreateOptionsMenu(menu: Menu, inflater: MenuInflater) {
        inflater.inflate(R.menu.list_menu, menu)
    }
	
	override fun onOptionsItemSelected(item: MenuItem): Boolean = when (item.itemId) {
        /* 
				Launch SearchDialog when "search" menu item is clicked.
				
				N/B: I chose to go with a SearchDialog instead of SearchView since it was easier for me 
				to send/pass custom app-data to my searchable activity (MainActivity in this case) after 
				submiting a search query
				*/
        R.id.menu_list_search -> activity?.onSearchRequested() ?: false
        else -> super.onOptionsItemSelected(item)
    }
}

SearchResultsFragment.kt

class SearchResultsFragment: Fragment(){
  private val args: SearchResultsFragmentArgs by navArgs()
  
  override fun onViewCreated(view: View, savedInstanceState: Bundle?) {
        super.onViewCreated(view, savedInstanceState)
        Log.i("SearchResultsFragment", "Received Query: ${args.query}")
    }
}