Hiding Admin Page While Keeping Menu Expanded

Actually, you just have to register your menu normally, with the declaration of the parent page like so:

function create_menu_and_submenu_page(){

    // Top level menu
    add_menu_page(
        'Books',
        'Books',
        'publish_posts',
        'books',
        'render_books_page',
        '',
        17
    );

    // Here the other subpages
    // ...

    // Submenu page
    add_submenu_page(
        'books',        // Here put the parent slug
        'Edit Book',
        'Edit Book',
        'publish_posts',
        'edit-book',
        'render_edit_book_page'
    );
}

And then, you simply have to hide it like that:

// We remove the unecessary links from the left menu
// while keeping the plugin menu selected
add_action( 'admin_head', function() {
    remove_submenu_page( 'books', 'edit-book' );  // 'parent-slug', 'subpage-slug'
} );

Hope it will help someone else in the future. Happy Coding :)

The solution is based on the ideas provided by @Ian. Thanks.

add_action( 'admin_menu', 'add_the_menus' );
function add_the_menus() {

    // Top level menu
    add_menu_page ('Books', 'Books', 'publish_posts', 'books', 'render_books_page', '', 17);

    // Adding this function to make the first submenu have a different name than the main menu
    add_submenu_page('books', 'Books', 'All Books', 'publish_posts', 'books', 'render_books_page' );

    if ((isset($_GET['page'])) && ($_GET['page'] === 'edit-book')) {
        // The Edit Book menu page and display it as the All Books page
        add_submenu_page('books', 'Edit Book', 'All Books', 'publish_posts', 'edit-book', 'render_edit_book_page' );
    }

    // The add-book menu page
    add_submenu_page('books', 'Add New Book', 'Add New', 'publish_posts', 'add-book', 'render_add_book_page' );
}

And we must hide the first menu item

add_action( 'admin_enqueue_scripts', function () {

    if ((isset($_GET['page'])) && ($_GET['page'] === 'edit-book')) {

        // Load CSS file
        wp_enqueue_style('book-edit', 'path/to/css/menu.css');

        // Load jQuery
        wp_enqueue_script('jquery');

        // Load 
        wp_enqueue_script('book-edit-script', 'path/to/js/menu.js');
    }
});

And the content of menu.css is:

#toplevel_page_books li.current {
    display: none;
}

#toplevel_page_books li.wp-first-item {
    display: list-item;
}

Also the content of 'menu.js' is:

jQuery(document).ready(function($) {

    $('#toplevel_page_books li.wp-first-item').addClass('current');

});

TL;DR

To understand how all this works, here is a step-by-step explanation.

Step 1: We add the main menu item (the books menu item) to display the list of books

add_action( 'admin_menu', 'add_the_menus' );
function add_the_menus() {

    // Top level menu
    add_menu_page ('Books', 'Books', 'publish_posts', 'books', 'render_books_page', '', 17);
}

Step 2: We add the add-book menu item as a submenu to the main books menu item

add_action( 'admin_menu', 'add_the_menus' );
function add_the_menus() {

    // Top level menu
    add_menu_page ('Books', 'Books', 'publish_posts', 'books', 'render_books_page', '', 17);

    // The add-book menu page
    add_submenu_page('books', 'Add New Book', 'Add New', 'publish_posts', 'add-book', 'render_add_book_page' );
}

Step 3: Finishing Step 2 above adds the books menu item, The menu list on the left side would look like this:

Books              <---------- This is the main top level menu names
  Books            <---------- This is the first sub-menu
  Add New          <---------- This is the second sub-menu

However, we should fix this. The intended list should look like this

Books              <---------- This is the main top level menu names
  All Books        <---------- This is the first sub-menu
  Add New          <---------- This is the second sub-menu

To do this, we have to modify our code as follows:

add_action( 'admin_menu', 'add_the_menus' );
function add_the_menus() {

    // Top level menu
    add_menu_page ('Books', 'Books', 'publish_posts', 'books', 'render_books_page', '', 17);

    // Adding this function to make the first submenu have a different name than the main menu
    add_submenu_page('books', 'Books', 'All Books', 'publish_posts', 'books', 'render_books_page' );

    // The add-book menu page
    add_submenu_page('books', 'Add New Book', 'Add New', 'publish_posts', 'add-book', 'render_add_book_page' );
}

Step 4: Next we should add a sub menu to edit books (the edit-book menu item). After adding his submenu, and when we are at the edit-book page, the menu on the left should look like this:

Books
  All Books        <---------- When we are in the 'edit-book' page, this menu item is selected and is highlighted (typically white in color), and also clicking on "All Books" would return us back to the "All Books" page.
  Add New

The solution I tried first was what I posted in my original question, which did not work exactly. So, based on discussions with @Ian and looking at his proposed solution, I came up with this:

add_action( 'admin_menu', 'add_the_menus' );
function add_the_menus() {

    // Top level menu
    add_menu_page ('Books', 'Books', 'publish_posts', 'books', 'render_books_page', '', 17);

    // Adding this function to make the first submenu have a different name than the main menu
    add_submenu_page('books', 'Books', 'All Books', 'publish_posts', 'books', 'render_books_page' );

    // If we are in the 'edit-book' page, then display the 'edit-book' submenu, otherwise, display the regular 'books' menu
    if ((isset($_GET['page'])) && ($_GET['page'] === 'edit-book')) {
        // Display the 'edit-book' menu page and display it as the 'all-books' page
        // Notice that the slug is 'edit-book', but the display name is 'All Books'
        add_submenu_page('books', 'Edit Book', 'All Books', 'publish_posts', 'edit-book', 'render_edit_book_page' );
    }

    // The add-book menu page
    add_submenu_page('books', 'Add New Book', 'Add New', 'publish_posts', 'add-book', 'render_add_book_page' );
}

Now, if we click on the 'books' menu item, or the 'add-book' menu item, then everything is fine. However, if we try to edit an existing book then the following menu list will be displayed

Books
  All Books        <---------- This is the first sub-menu (due to the first submenu call)
  All Books        <---------- This is the 'edit-book' page (HIGHLIGHTED)
  Add New

Step 5: Now we notice the following: By clicking on the first submenu, the "All Books" page will be rendered, and clicking on the second submenu will render the "Edit" page; and in our case, we want to render the "All Books" page. Therefore, we have to hide the SECOND submenu and make the first submenu highlighted. This is done as follows:

add_action( 'admin_enqueue_scripts', function () {

    if ((isset($_GET['page'])) && ($_GET['page'] === 'edit-book')) {

        // Load CSS file
        wp_enqueue_style('book-edit', 'path/to/css/menu.css');

        // Load jQuery
        wp_enqueue_script('jquery');

        // Load 
        wp_enqueue_script('book-edit-script', 'path/to/js/menu.js');
    }
});

And the content of menu.css is:

#toplevel_page_books li.current {
    display: none;
}

#toplevel_page_books li.wp-first-item {
    display: list-item;
}

Also the content of 'menu.js' is:

jQuery(document).ready(function($) {

    $('#toplevel_page_books li.wp-first-item').addClass('current');

});

And now everything works like a charm.

For your particular situation, where you need to have a menu registered, but not shown unless you click on it from a link on another page you can add a conditional check to see if you're on the editing page. If so, then change replace null with book per the add_submenu_page() parameters.

add_action( 'admin_menu', 'add_the_menus' );
function add_the_menus() {

    // Top level menu
    add_menu_page( 'Books', 'Books', 'publish_posts', 'books', 'render_books_page', '', 17 );

    // Adding this function to make the first submenu have a different name than the main menu
    add_submenu_page( 'books', 'Books', 'All Books', 'publish_posts', 'books', 'render_books_page' );

    // The Add Book menu page
    add_submenu_page( 'books', 'Add New Book', 'Add Book', 'publish_posts', 'add-book', 'render_add_book_page' );

    // Check the get parameter for page to see if its the page you want to display in the menu only when you're on it.
    if ( $_GET['page'] === 'edit-book' ) {
        // The Edit Book menu page (this page is hidden from the menu, and accessed via the All Books page only)
        add_submenu_page( 'books', 'Edit Book', 'Edit Book', 'publish_posts', 'edit-book', 'render_edit_book_page' );
    } else {
        // The Edit Book menu page (this page is hidden from the menu, and accessed via the All Books page only)
        add_submenu_page( null, 'Edit Book', 'Edit Book', 'publish_posts', 'edit-book', 'render_edit_book_page' );
    }
}

An additional note. If it turns out that you need to also keep that menu item hidden even when selected you can enqueue a style to hide it only when you're on that page.

add_action( 'admin_enqueue_scripts', function () {
    if ( $_GET['page'] === 'edit-book' ) {
        wp_enqueue_style( 'book-edit', get_stylesheet_directory_uri() . '/assets/css/book-edit.css' );
    }
} );

Where the contents of book-edit.css would be something as simple as:

#toplevel_page_books li.current {
    display: none;
}