Initialize to nested screen with back button to stack root in react-native using react-navigation

I am using React Native and the React-Navigation library to replicate the nav behavior in the iOS Reddit app Apollo: https://i.imgur.com/983G04Q.png

My routing structure is as follows:

TabNavigation
|- PostsTab
  |- PostsStack
    |- SubredditListScreen
    |- PostFeedScreen
    |- PostDetailsScreen

I want to achieve the following:

• When the app starts, the user sees the PostFeedScreen.
• The PostFeedScreen has a "Back" button in its header that navigates to the SubredditListScreen.
• If the PostsTab tab bar is pressed when on PostFeedScreen, scroll to the top, and if already at the top, navigate to the SubredditListScreen.
• The SubredditListScreen doesn't have a back button, but the user can drag from the right-edge to return to the PostFeedScreen.

This is the code I have:

// TabNavigation.tsx

function TabNavigation() {
  return (
    <Tab.Navigator>
      <Tab.Screen name={SCREENS.POSTS} component={PostsStackScreen} />
      // ..other non-relevant tabs
    </Tab.Navigator>
  );
}

// PostsStackScreen.tsx

function PostsStackScreen() {
  return (
    <PostsStack.Navigator initialRouteName={SCREENS.POSTS_FEED}>
      <PostsStack.Screen name={SCREENS.SUBREDDITS_LIST} component={SubredditsScreen} />
      <PostsStack.Screen name={SCREENS.POSTS_FEED} component={PostFeedScreen} />
      <PostsStack.Screen name={SCREENS.POST_DETAILS} component={PostDetailsScreen} />
    </PostsStack.Navigator>
  );
}

However, my code doesn't work as expected:

• The app correctly initializes to the PostFeedScreen, but there is no "Back" button to the Subreddits screen.
• Clicking the tab button doesn't take the user to the Subreddits screen.

How can I accomplish the above with React-Navigation? Thank you!