I tried the following code, but when I display ScreenCommon, the BottomNavigationItem is deselected.

NavHost(navController = navController, startDestination = "tab1") {
    navigation(startDestination = "screen_a", route = "tab1") {
        composable("screen_a") { /* */ }
        composable("screen_b") { /* */ }
    }
    navigation(startDestination = "screen_c", route = "tab2") {
        composable("screen_c") { /* */ }
        composable("screen_d") { /* */ }
    }
    composable("screen_common") { /* */ }
}

BottomNavigationItem is implemented as follows. Same as the document.

BottomNavigationItem(
    selected = currentDestination?.hierarchy?.any { it.route == tab.route } == true,
    // ...
)

If you want to track the last selected bottom nav item and use that as the source of truth for what tab is selected (and not use the current destination for that source of truth), there's nothing stopping you from writing that code

Fixed

BottomNavigation {
    var selectedIndex by rememberSaveable { mutableStateOf(0) }

    tabs.forEachIndexed { index, tab ->
        BottomNavigationItem(
            selected = selectedIndex == index,
            onClick = {
                if (selectedIndex == index) {
                    (navController.findDestination(tab.route) as? NavGraph)?.let {
                        navController.popBackStack(it.startDestinationId, false)
                    }
                } else {
                    navController.navigate(tab.route) {
                        popUpTo(navController.graph.id) {
                            saveState = true
                        }
                        launchSingleTop = true
                        restoreState = true
                    }
                    selectedIndex = index
                }
            },
            icon = {
                Icon(imageVector = tab.icon, contentDescription = null)
            },
            label = {
                Text(text = tab.label)
            },
        )
    }
}