Is it good practice using two navigation (component architecture) in the same app?

This might help you In theory, the Navigation library supports any architecture you might want to use. Out of the box it can handle Activities and Fragments as navigation destinations, but you can plug in your own solution by implementing your own Navigator (as an example, see this article).
However, quoted / paraphrased from the Google I/O talk on Navigation:

will help you UPDATE: I don't recommend this approach any more. For small apps it may work for you, but I ran into complications when trying to pass data between different navigation graphs hosted inside different NavHostFragments. I think the easiest route is the "hack" of hiding fragments in your top level layout to allow a full screen view. You can add an addOnDestinationChangedListener to listen for destinations that you want full screen, and simply hide the fragment required.
ORIGINAL ANSWER: I do it like this in my app and it works well. You should wrap all your current fragments in a parent fragment with a main_nav_graph.xml. For example:

<androidx.constraintlayout.widget.ConstraintLayout
    xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    android:layout_width="match_parent"
    android:layout_height="match_parent">

    <fragment
        android:id="@+id/main_host_fragment"
        android:name="androidx.navigation.fragment.NavHostFragment"
        android:layout_width="match_parent"
        android:layout_height="match_parent"
        app:defaultNavHost="true"
        app:navGraph="@navigation/main_nav_graph" />

</androidx.constraintlayout.widget.ConstraintLayout>

<navigation xmlns:android="http://schemas.android.com/apk/res/android"
    xmlns:app="http://schemas.android.com/apk/res-auto"
    xmlns:tools="http://schemas.android.com/tools"
    android:id="@+id/main_nav_graph.xml"
    app:startDestination="@id/main_fullscreen">

    <fragment
        android:id="@+id/main_fullscreen"
        android:name="com.example.myapplication.MainFullscreen" >

        <action
            android:id="@+id/action_main_fullscreen_to_fullscreen2"
            app:destination="@id/fullscreen2" />

    </fragment>

    <fragment
        android:id="@+id/fullscreen2"
        android:name="com.example.myapplication.Fullscreen2" />
</navigation>

Navigation.findNavController(activity!!, R.id.main_host_fragment).navigate(R.id.action_main_fullscreen_to_fullscreen2)

fixed the issue. Will look into that further No need of writing separate code to replace the back button with the drawer icon.
In AppBarConfiguration pass the fragment ids (from nav_graph) which you are using to navigate from both bottom navigation & navigation drawer. (P.S fragments and its associated icon should have same ids)

appBarConfig = AppBarConfiguration.Builder(R.id.starFragment, R.id.statsFragment, R.id.userFragment)
                .setDrawerLayout(drawerLayout)
                .build()

setSupportActionBar(toolbar)
setupActionBarWithNavController(navController, appBarConfig)

navView.setupWithNavController(navController)
bottomNav.setupWithNavController(navController)

override fun onSupportNavigateUp(): Boolean {
        return navController.navigateUp(appBarConfig)
    }

override fun onBackPressed() {
        if (drawerLayout.isDrawerOpen(GravityCompat.START)) {
            drawerLayout.closeDrawer(GravityCompat.START)
        } else {
            super.onBackPressed()
        }
    }

<menu xmlns:android="http://schemas.android.com/apk/res/android">
    <item
        android:id="@+id/starFragment"
        android:icon="@drawable/ic_star_green_48dp"
        android:title="@string/bottom_nav_title_star"
        android:menuCategory="secondary"/>
    <item
        android:id="@+id/statsFragment"
        android:icon="@drawable/ic_stats_green_48dp"
        android:title="@string/bottom_nav_title_stats"
        android:menuCategory="secondary"/>
    <item
        android:id="@+id/userFragment"
        android:icon="@drawable/ic_user_green_48dp"
        android:title="@string/bottom_nav_title_user"
        android:menuCategory="secondary"/>
</menu>

To fix the issue you can do As mentioned in the documentation :

I hope this helps . I had the same issue with navigation version 1.0.0-alpha08. I have solved it by re-implementing setupActionBarWithNavController to provide the custom behaviour that I needed.

setDisplayShowTitleEnabled(false) //Disable the default title

container.findNavController().addOnDestinationChangedListener { _, destination: NavDestination, _ ->
    //Set the toolbar text (I've placed a TextView within the AppBar, which is being referenced here)
    toolbar_text.text = destination.label

    //Set home icon
    supportActionBar?.apply {
        setDisplayHomeAsUpEnabled((destination.id in NO_HOME_ICON_FRAGMENTS).not())
        setHomeAsUpIndicator(if (destination.id in TOP_LEVEL_FRAGMENTS) R.drawable.app_close_ic else 0)
    }
}